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A random number generator picks a number from one to nine in a uniform manner.
a. Graph the probability distribution.
b. $f(x)=$
c. $\mu=$
d. $\sigma=$
e. $P(3.5<x<7.25)=$
f. $P(x>5.67)$
g. $P(x>5 | x>3)=$

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Let $ f(x) = 30x^2 (1 – x)^2 $ for $ 0 \le x \le 1 $ and $ f(x) = 0 $ for all other values of $ x $.(a) Verify that $ f $ is a probability density function.(b) Find $ P(X \le \frac{1}{3}) $.



Show that each function defined as follows is a probability density function on the given interval; then find the indicated probabilities.$(x)=\frac{1}{4}(1+x)^{-5 / 4} ;[0, \infty)$(a) $P(0 \leq X \leq 2)$ (b) $P(1 \leq X \leq 3)$ (c) $P(X \geq 5)$



I am David and I’m here to have your answering your question. Now let me bring up your question here and the question when she describes abandoned uniform distribution, let me remind you that we have X followed by the uniform from HP. And then the density on the X. is equal to one over B -A. For the anc’s between the A. And B. Now We have asked if we followed by the uniform from the 1-9 and therefore F. X. Echo to one another nine months one which is equal to 1/8 X. Kirby between the one and nine. Now in the pot we have just get the graph of the pdf. So it would do it here. This will be let’s say one out of eight 012345678 nine. This will be one. So that then stay off the function. It will be this one. Oh yeah. And then we go here and this will be the F. Of X. And now there be we will have the so this one will be the density. But I think the question also asking her to find distribution function. So the distribution function will be increasing up to kenya and then go to sorry, it should be the only one around. So let me do it in the seventh graf now. So the distribution, it will be the capital f. So this will be one here and then one Nutri from 56789. And then we will have the graph that looks like starting from here and then on the way it got you the one and then going here there could be the distribution probability function now for the B. Once you find the mean and the uh be asking her to find F. X. So we’ve had the mx already now. So I will write in again F. X. Echo 21 of eight. For the X. Between the 1 to 9. It could be otherwise. Now for the C. Once you find the mean of the act which is A. In the act, My family will be a Plus B divided by two. So we have echo to the one…

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