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Let X be a discrete random variable with the probability distribution function given belowP(X=x)ionthen p(0 <X <3.1)6 3 2None...

Question

Let X be a discrete random variable with the probability distribution function given belowP(X=x)ionthen p(0 <X <3.1)6 3 2None

Let X be a discrete random variable with the probability distribution function given below P(X=x) ion then p(0 <X <3.1) 6 3 2 None



Answers

Assume that $x$ has a normal distribution with the specified mean and standard deviation. Find the indicated probabilities.$$P(3 \leq x \leq 6) ; \mu=4 ; \sigma=2$$

All right, We have normal distribution acts with mean four and standard deviation to. We want to find the probability that X lies between three and six. We're going to solve this problem in terms of Z scores, which makes the standard normal distribution easier to understand to start off with. Let's remember that a Z score is by definition x minus the mean, divided by the standard deviation. We can convert the two bounds for this probability to Z scores. Using this formula first for Z one, we have three minus 4/2 equals negative one half, and secondly we have Z equals six minus 4/2 equals one. So now we can restate this problem as the probability that the Z score falls between negative one half and one, or the probability that Z is less than equal to one minus the probability Z is less than negative 10.5. This second restating of the probabilities. In terms of Z scores allows us to use a Z table look up in order to identify this problem. So using a Z table, we find these quantities equal 2.8413 minus 0.3085 which gives us our final probability of 0.53 to eight.

Mhm. The probability that the random variable Is greater than or equal to two Equals the probability that it equals two Plus the probability that it was three plus the probability that it calls for and they're psychos point to first point to plus point to Rich People's .6. Be careful and its expectation. He calls the son of the value of the outside times. Its probability, Which he goes one times .4 plus joe times point to Plus three times point to Plus four times point to okay. And this equals 0.4 plus 0.4 plus 0.6 plus 0.8 where she goes two points to

Mhm. According to the definition, the probability that the random variable X. Is greater than we called you, too, because The probability that equals two plus the probability the articles. Mhm. Which vehicles .05 plus .05 Read trickles .1. Mhm. Mhm. And the expectation he calls the south of exciting times its probability. And so there's Eco's zero times 0.8, last one times, mhm 0.1 plus two times .05 Plus three times .05. And this tickles .35 Yeah, participation.

So the whole theme in this problem is that your expected value? You know, I'll straight X. And P. Is this is the probability that you'll land on zero or you'll get zero points Maybe like you're playing a dark game, uh if you land on a certain spot is 50% of the time, you get zero points And then you're 20% of the time, you get one And then 20% of the time you get to. And then but The remaining 10% music would land on three. So the whole premise of the expected value of getting that is multiplying. So you would expect to get zero points 50% of the time. You expect to get 1.20% of the time And then uh two points 20% of the time and then three points 10% of the time. This is how you approach the problem. And this isn't too bad because zero times anything is just that thing and one times anything is just that thing. So 0.2 plus 0.4 plus 0.3, I would expect to get just ran through it at the board or whatever game it is Point to .4.6 plus .3, That's how you get the answer.


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