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1. Let X be a continuous random variable with probability density function f(x) = { if...
4. Let X be a continuous random variable with probability density function: x<1 0, if if| if x>4 f(x) = (x2 + 1), 4 x 24 0 Find the standard deviation of random variable X.
b. Let X be a continuous random variable with probability density function f(x) = kx2 if – 1 < x < 2 ) otherwise Find k, and then find P(|X| > 1/2).
3. Let X be a continuous random variable with probability density function ax2 + bx f(0) = -{ { for 0 < x <1 otherwise 0 where a and b are constants. If E(X) = 0.75, find a, b, and Var(X). 4. Show that an exponential random variable is memoryless. That is, if X is exponential with parameter > 0, then P(X > s+t | X > s) = P(X > t) for s,t> 0 Hint: see example 5.1 in...
2x 0<x<1 Let X be a continuous random variable with probability density function f(x)= To else The cumulative distribution function is F(x). Find EX.
2. Let U be a continuous random variable with the following probability density function: g(t) = 1+t -1 <t < 0 1-t 0<t<1 0 otherwise a. Verify that g(t) is indeed a probability density function. [5] b. Compute the expected value, E(U), and variance, V(U), of U. (10)
Let X be a continuous random variable with the following probability density function f 0 < x < 1 otherwise 0 Let Y = 10 X: (give answer to two places past decimal) 1. Find the median (50th percentile) of Y. Submit an answer Tries 0/99 2. Compute p (Y' <1). Submit an answer Tries 0/99 3. Compute E (X). 0.60 Submit an answer Answer Submitted: Your final submission will be graded after the due date. Tries 1/99 Previous attempts...
Suppose that X is a continuous random variable whose probability density function is given by (C(4x sa f(x) - 0 otherwise a) What is the value of C? b) Find PX> 1)
Let X be a continuous random variable with the following density function. Find E(X) and var(X). 6e -7x for x>0 f(x) = { for xso 6 E(X) = 49 var(X) =
Let X be a continuous random variable with density f(x) = e?5x, x > b. Find b. A. (ln 5)=5 B. ?(ln 5)=5 C. e?5=5 quad D. 3 E. None of the preceding Let X be a continuous random variable with density f(x) = e-5x, x > b. Find b. A. (In 5)/5 B. — (In 5)/5 C. e-5/5 quad D. 3 E. none of the preceding
2te-t2 = { t> 0 6. Let g(t) be the probability density function of the continuous 0 t < 0 random variable X. a. Verify that g(t) is indeed a probability density function. [8] b. Find the median of X, i.e. the number m such that P(X 5 m) = į = 0.5. [7]