The table below shows a probability density function for a discrete random variable X. What is the probability that X is 2? P(X = x) 1/12 1 5/12 2 1/12 3. 1/6 1/6 1/12

Suppose a discrete random variable W has the following probability mass function (where c > 0 is a constant): w 1 2 3 5c p(w) 20 4 2 4 (a) What is the value of c? (b) Find the standard deviation of W.

A probability function for a discrete random variable, Y, is shown below.     y P(Y=y) 4 0.4 6 0.2 8 0.2 10 0.2   Show how you would calculate the mean of Y. (You do NOT need to work this out). μ=

The probability density function of a discrete random variable X is given by the following table: Px(X = 1) = .05 Px(X = 2) = .10 Px(X = 3) = .12 Px(X = 4) = .30 Px (X = 5) = .30 Px (X = 6) = .1i Px (X = 7) = .01 Px(X = 8) = .01 i) Compute E(X). ii) Compute Var(X). iii) Compute Px(X 3)

Let X be a random variable whose probability density function is plotted below. If one was to generate X by passing a uniform (0, 1) random variable through a function, then what function would you use? (your answer should be a function of x). 0.9- 0.8- 0.7- 0.6- 0.5 qula Snip 0.4 0.3- 0.2- 0.1 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0

Suppose the random variable X has the following probability density function f (x) = 0Sロs2 2 lo otherwise What is the expected value of X? O 2/9 O 1 O 3/4 O 4/3

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let x be a discrete random variable with probability function p(x)= cx/20 for x = 2,3,4,5,6,8,12 what is the value of c that makes p(x) a valid probability function?

The figure above shows the probability density function for the random variable x. What is P(3≤x<7)?

Y is a continuous random variable with the probability density function pictured. what is the mean of y?