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Let X1 the amount oftime You wait for the subway on your way t0 work andxz th? amount of time you wait for your caffce on th? way to work (both in minutes) Thejoin...

Question

Let X1 the amount oftime You wait for the subway on your way t0 work andxz th? amount of time you wait for your caffce on th? way to work (both in minutes) Thejoint pmf of Xi andxz given as:Let X3 be the total walt limeFind EX3)

Let X1 the amount oftime You wait for the subway on your way t0 work andxz th? amount of time you wait for your caffce on th? way to work (both in minutes) Thejoint pmf of Xi andxz given as: Let X3 be the total walt lime Find EX3)



Answers

Let $X$ have the $\operatorname{pmf} p(x)=\left(\frac{1}{2}\right)^{x}, x=1,2,3, \ldots$, zero elsewhere. Find the pmf of $Y=X^{3}$.

And problem seven. We have the probability mass function for the random variable X equals one third. When X equals want to All three and it equals zero elsewhere. We want to find the probability mass function for the random variable boy where it equals two X plus one. You Why in the X is want one. Which means we can get X as a variable voice where X equals Why -1 divided by two. Then we can get we avoid by substituting here and replace each X By Why -1 divided by two. As long as here we don't have six, then just 1/3 ends you. It's one third when X equals 123 Let's substitute by X. Here. In the function to get Y equals to multiply by one plus one, gives the three Then five and 7. And it's legal else with. And this is the final answer of our problem.

Problem. Then we have the probability mass function for the random variable X, which is defined as one half to the bar of the absolute value of X when x equals -1 -2 -3. and so we want to find the probability mass function for the random variable Y, which is defined as X to the power of four. For the stated values of X. You can find that why? And X is want one. Each value of X here corresponds to a unique value, avoid. But we notice that to get X as a function of boy, we should get the negative branch of why? It was about one divided by four. Of course this negative sign and not make any difference because we have here an absolute but we should know that we take the negative branch because we have here the negative values of X As long as X&Y is want one. Then we can find B. Why sequence Why? By substituting by the value of X Year By this exhibition. Then it's 1/2 to the power of the absolute of minus Y. Should be small. White To the power of one divided by four. And the values of Y. We substitute here by each value of X. We substitute, then swamp and two. It was about four 16, then It's 81 and so on. These are the only possible values that we can substitute in our function and we can rewrite it as half. It is a bar of why one quarter? Because the absolute function doesn't make any difference with this. Find the sign. And we knew that Why here is always supposed.

In Problem 75. We have a subway train on the red line that arrives every eight minutes. Every eight minutes arrives a train subway train in the red light during rush hours for birthday, we want to define the random variable. We are interested in the length of time a commuter must wait for a train to arrive. This means the random variable X is the time that a commuter, most with for a subgroup three train and on the red line on the red on the red line for birdie. We want to grab the probability distribution given in the problem. The time follows are informed distribution. Then there probability distribution we have here claim. And here the probability density function. If X and it's uniform, this is a great football. See, we want to define the probability density function F of X equals one divided by P minus a where B is the maximum in the interval and they is the minimum. The maximum time that a computer can wait is eight minutes, because if he just missed a train, he will wait for eight minutes for the next train to arrive than the equals eight minutes and e equals, of course, zero. Because he might arrive just at the time the train arrives. Then he will not wait. Then the probability, Dennis the probability density function. We have one divided by B minus A. B is eight minus zero equals one divided by it. Then we can and here one divided by eight. Well, the function here is in minutes. Wonderful. Sorry. Minutes is the time in minutes here, and it starts at zero and then at it then X is greater than or equal zero and smaller than recalls eight minutes for body. We want to calculate the mean the mean for the uniform. Inspiration is average between the lower and upper bounds or limits people as a divided by two eight plus zero divided by two equals four minutes. See mm, you won't. That's standard deviation. The Standard and Division is the square root of B minus K Square two. Divided by 12. This is a formula for the standard for the standard division, for the the only form of distribution. Square root of eight by 80 square divided by 12 equals 2.31 minutes for 2.3 for birth F. We want to find the probability that the commuter weights it's one minute The probability for ex for the random were able to be less than one minute. We can go back two the grip of the probability distribution and calculate the area under the curve at the equals one. Then here AT T equals one. Let's calculate this area. It's just the area of a triangle, one multiplied by one. Divided by it then equals one minus zero, multiplied by the probability she's one divided by it equals one. Buy it, buy it for birth. G. We want to find the probability that the commuter waits between three and four minutes. Probability for the random were able to be between three and four minutes equals. We can do the same. Enter the probability grave from 3 to 4 here, for example, and to get this area there is another approach is to get the area from 4 to 0, then subtract from it area from T 20 and we will have the same to get the area. Under the probability distribution killed, we multiply the base, which is four minus three, which is one multiplied by the height, which is the probability distribution on the possibility that the very then it's a four minus three multiplied by F of X which is one divided by eight, equals one by the by it. And these are the final answers of our problem, the grave and the definition of the random very.

Problem line. We have the probability mass function for the random variable X. That is defined as B of x equals x equals one third X equals -10 and one. We want to find the probability mass function of void, which equals x squared for the stated values of X. We can find that. Why is not want one with X? Because every value here doesn't have a unique value of boy. Let's get The values that correspond to -100 and one. When we substitute here we get values avoid equals one zero and one. Then We have only two possible values of Y Which are zero and 1. Then to find the probability avoid equal zero comes when X equals E, Which is one thing. But the probability For why equals one comes when X equals minus one or X equals one. Then we should add proof of edits, then equals X equals the probability with X equals minus one, Plus the probability of x equals one equals one third plus one third equals two thirds. Then, to sum up, we can get the probability of boy equals Y, two equals one third, when why equals zero and two thirds when Y equals what? And this is a final answer of our problem.


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