Let a random variable X have the p.f. f(x) = c(|x| + 1)^2 for x = 0, ±1. Find the constant c so that f(x) is a valid probability function. Then, find E(X), E(X^2 ) and var(X).
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Let a random variable X have the p.f. f(x) = c(|x| + 1)2 for x = 0, ±1. Find the constant c so that f(x) is a valid probability function. Then, find E(X), E(X2 ) and var(X).
1. 20 points Let X be a random variable with the following probability density function: f(x)--e+1" with ? > 0, ? > 0, constants x > ?, (a) 5 points Find the value of constant c that makes f(x) a valid probability mass function. (b) 5 points Find the cumulative distribution function (CDF) of X.
1. (15 points) Let X be a continuous random variable with probability density function f (x) c(1-), 0 < 1, where c is a constant. i) Find the constant c ii) What is the distribution function of X? ii) Let Y 1x<0.5 Find the conditional expectation E(X|Y). 1. (15 points) Let X be a continuous random variable with probability density function f (x) c(1-), 0
1. Let X be a continuous random variable with probability density function f(x) = { if x > 2 otherwise 0 Check that f(-x) is indeed a probability density function. Find P(X > 5) and E[X]. 2. Let X be a continuous random variable with probability density function f(x) = = { SE otherwise where c is a constant. Find c, and E[X].
Let X have probability density function f(2)= k(1+x) -3 for 0 < x < oo and f(x) = 0 elsewhere. a. Find the constant k and Find the c.d.f. of X. b. Find the expected value and the variance of X. Are both well defined? c. Suppose you are required to generate a random variable X with the probability density function f(x). You have available to you a computer program that will generate a random variable U having a U[0,...
Problem 1. (a) Let X be a Binomial random variable such that E(X) 4 and Var(x) 2. Find the parameters of X (b) Let X be a standard normal random variable. Write down one function f(t) so that the random variable Y-f(X) is normal with mean a and variance b.
3. Let X be random variable with probability density function x(x)4 for 0 x 1, (Note: fx (x) = 0 outside this domain.) (a) Find E[X] and Var[X] (b) Let Y- X2 +5. Find E[Y] and Var[Y]. (c) Find PX 112 ).
5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f find a and b. (b) Give the cumulative distribution function F,(x) f()dt of X and Var(X) (c) Let A be any Borel set of R. Define P by P(A) [,f dm 5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f find a and b. (b) Give the cumulative distribution...
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) =
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...
Let the random variable X and Y have joint pdf f(x,y)=4/7(x2 +3y2), 0<x<1, 0<y<1 a. find E(X) and E(Y) b. find Var(X) and Var(Y) c. find Cov (X,Y)