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Let X denote the number of cars thar Cross over particular bridge in one minute: Suppose the distribution of x is given by:00.4Calculate tne expected value: U; of x...

Question

Let X denote the number of cars thar Cross over particular bridge in one minute: Suppose the distribution of x is given by:00.4Calculate tne expected value: U; of xCalculate tne varianceofx

Let X denote the number of cars thar Cross over particular bridge in one minute: Suppose the distribution of x is given by: 00.4 Calculate tne expected value: U; of x Calculate tne variance ofx



Answers

A dealer's profit, in units of $\$ 5000,$ on a new automobile is a random variable $X$ having the density function given in Exercise 4.12 on page $137 .$ Find the variance of $X$.

Said this question. You know, assuming Zehr let why were they random variable, which represents the totally number off cars entering the green room? All right, now, uh, therefore I can write down that Why can't build on us since submission from my eyes 123 And this would be given by Ex I. So finances in the proper form is a vey good rex one plus x school this x three and there's some data I've just been given. Wasn't the questions I just write down that we've been given that expectation off X one is 800. An expectation off extra cool is 1000. Expectation of X three is 600. Then I have radios off x one. There's given a 16 square than bearings. Off extra will be 25 square ingredients of extremely because these are the standard delusion squares which will be equal to eating square now to find out the expectation off why I'm starting with the first part here. So to find out the expectation off by using the linearity property, I can work here right on that You off x one plus extra bless X tree cannot actually voted in as your ex one. Bless you off x two. Bless ye off x three. So if you are in all the values by substituting harnesses 800 plus, I have 1000 unless this is 600 if you add them, then the expectation of five you're getting is true, Colin 400. Next Just to find from Barbie, we're supposed to find a radiance off. Why so for the part be writing her millions off while using the properties we can write down, This would be equal to BU off x one plus view of X two presently off X tree. So this is equal to 16 square. Bless grim defy square. Plus, I have 18 square your square, and I have them in the value We're getting heroes 105 not moving on to the bar to see in the park. See, they're saying that you take if available, that dependent here are no. So we said that the linearity property off expected value walls even if the variables involved are dependent. So I could say that though, dean your property off the expected value whores, even if the variables are dependent. Okay. And so the competition from body still hordes? No uh, less. Well, I'll be off extra pleasant review off X tree. Then I'll have plus twice off. Cool aliens off X one extra plus twice off core Aidan's off X two x tree and bless price core billions off extremely x one. So substituting the values that we have this is 16 square best 25 square plus 18 square. Then bless this is price off Corwin's of exotic stories. 80 plus twice off. Oh, billions of extra X three years 100 and dries off billions of extra. The X one is 90. So you squared and add all the other terms were getting down. Said he had us 1745. This is Radiance off. Why that we have got for dependent variables and from this, I can therefore find understand indication off. I also will be squared off this millions of square root of 17 for fight, so the answer will be equal do for one point 77

In this problem, it is given that the number of customers who enter a bank in an hour is a poison random variable. Let X denote the number of customers who enter the bank in an hour. And suppose that probability of x equal to zero is equal to 0.05. We have to determine the mean and variance of X. We know that probability of X equal to X is the rest to minus Lombardi. Lombardi, rest two X divided by X. Factorial. We are x ranges from 01 up to infinity. So we will find probability of X equal to zero. Using this formula Probability of x equal to zero. There will be, It is 2- Lamberti Lamberti raised two x. But here X equal to zero. So Lambright erased. 20 divided by X. Factorial. That this divided was zero factorial, But probability of x equal to zero is given to be 0.05. We will use this value so zero point zero faith is equal to he reached to minus lamb bratty laboratories to zero is one and zero factorial is also one, so it is two minus Lamberti into one divided by one which is again it is two minus landlady. We will take natural log on both sides. So Ellen of 0.05 is equal to Ellen off erased. Too minus Lamberti. Natural law of 0.05 is minus two point 99 57. This is equal to natural log of eras, tu minus limb, bratty is minus Lamberti. Multiplying the -1 on both sides. We get to point 99 57 is equal to Lamberti. We have to determine the mean and variance of X. We know dad mean of X. That is expected, eggs is equal to Lamberti. If X follows poison distribution, expected X is equal to Lamberti which is equal to two point 99 57. Also variants of X is equal to Lamberti for poison, and the variable X variants of X is also equal to land property. This is equal to two point 99 57, So mean of X is 2.9957, and variance of X is also 2.9957.

In this problem, it is given that the number of customers who enter a bank in an hour is a poison random variable. Let X denote the number of customers who enter the bank in an hour. And suppose that probability of x equal to zero is equal to 0.05. We have to determine the mean and variance of X. We know that probability of X equal to X is the rest to minus Lombardi. Lombardi, rest two X divided by X. Factorial. We are x ranges from 01 up to infinity. So we will find probability of X equal to zero. Using this formula Probability of x equal to zero. There will be, It is 2- Lamberti Lamberti raised two x. But here X equal to zero. So Lambright erased. 20 divided by X. Factorial. That this divided was zero factorial, But probability of x equal to zero is given to be 0.05. We will use this value so zero point zero faith is equal to he reached to minus lamb bratty laboratories to zero is one and zero factorial is also one, so it is two minus Lamberti into one divided by one which is again it is two minus landlady. We will take natural log on both sides. So Ellen of 0.05 is equal to Ellen off erased. Too minus Lamberti. Natural law of 0.05 is minus two point 99 57. This is equal to natural log of eras, tu minus limb, bratty is minus Lamberti. Multiplying the -1 on both sides. We get to point 99 57 is equal to Lamberti. We have to determine the mean and variance of X. We know dad mean of X. That is expected, eggs is equal to Lamberti. If X follows poison distribution, expected X is equal to Lamberti which is equal to two point 99 57. Also variants of X is equal to Lamberti for poison, and the variable X variants of X is also equal to land property. This is equal to two point 99 57, So mean of X is 2.9957, and variance of X is also 2.9957.

Will come to enumerate. In the current problem we have two variables x. And Well, now X is the number of automobiles that arrive in any one minute in Durban that arrived in. You need one minute in turban and it is given that X follows a partial distribution with lambda and expectation of X is equals two. We know the by formula is lambda but is given to be five. The lambda is equals 25 Now we are asked that what is the probability that X at least five automobiles Are coming, correct? five. So the number is five years, but at least five. The probability exist 567 Anything so that we can summarize that probability X greater than equals 25 which can be written us one minus probability X less than equal to food. So if we substitute in the p m f of X and obtain the values we will have. It's the power minus five plus. It was the power minus five into five. To the power one by one factorial. This is probability of one plus, this is probably a zero of course. And same way probability of two which will be to the power minus five into five squared by two factorial. Then it's the power minus 55 Q by three factorial. And it is the power minus five into five. To the power by four factorial. Now if we plug in all these values and calculated the final value would be zero point 44 04 Now. No on the other hand, why is the variable which is defined by inter arrival time? That means between on a more on one minute there there will be like some number of vehicles coming sometimes zero, sometimes one. So inter arrival time will be between any two successive arrivals, Right? Any two successive arrivals. And it is also mentioned that why follows an exponential distribution? And for exponential distribution, it is mentioned that on an average it is expected that the time of uh this value of expectation of Y is one by five. Now we know for an exponential theater The expense expectation is one x 3 to Therefore Theta is equal to five. So food. Why? If of what it is Theatre You to keep our -3 to eggs for ex greater than gold to zero and zero. Other ones which can be uncertain as Five to take our -5 picks for accident about equal to zero and zero otherwise. So how can we obtain the program? Is that it means at least uh does not exceed, does not exceed one x 5 minutes. Now the intolerable time it cannot be negative. And to be honest, exponential distribution always starts from 00 to one x 55. It was the power -5 x. Dx correct. So five in two. Now how do we do it with the power M. X divided by him. So it was about minus five X divided by minus five ranges from 0 to one by five. So how will be evaluated C 55 cancels So it is minus it was the power of minus five into one by five minus minus. It is the power minus five in 20 correct? So we will have minus, it will be powered now. 55 cancel. So we get minus one plus it's the power zero. Anything reasonable zero is far so- It's about minus. Well now if we evaluate this in calculator we get 0.63 212056. So I hope you can understand this. And for your information if you see I'm using very uh large decimal places so that you can round it off up to your city


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