# Question

Let X be a random variable that takes on values between 0 and c. That is, P{0 ≤ X ≤ c} = 1.

Show that

Var(X) ≤ c2/4

One approach is to first argue that

E[X2] ≤ cE[X]

and then use this inequality to show that

Var(X) ≤ c2[α(1 − α)] where α =E[X]/c

Show that

Var(X) ≤ c2/4

One approach is to first argue that

E[X2] ≤ cE[X]

and then use this inequality to show that

Var(X) ≤ c2[α(1 − α)] where α =E[X]/c

## Answer to relevant Questions

Show that Z is a standard normal random variable, then, for x > 0, (a) P{Z > x} = P{Z < −x}; (b) P{|Z| > x} = 2P{Z > x}; (c) P{|Z| < x} = 2P{Z < x} − 1. Two points are selected randomly on a line of length L so as to be on opposite sides of the midpoint of the line. [In other words, the two points X and Y are independent random variables such that X is uniformly distributed ...Consider independent trials, each of which results in outcome i, i = 0, 1, . . . , k, with probability pi, Let N denote the number of trials needed to obtain an outcome that is not equal to 0, and let X be that outcome. (a) ...The expected number of typographical errors on a page of a certain magazine is .2. What is the probability that an article of 10 pages contains (a) 0 and (b) 2 or more typographical errors? Explain your reasoning! If X1, X2, X3 are independent random variables that are uniformly distributed over (0, 1), compute the probability that the largest of the three is greater than the sum of the other two.Post your question

0