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4. Let X be a continuous random variable with probability density 1 0< x<3 -x + k =6 f(x) elsewhere 0, Evaluate k...
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].
3. Let X be a continuous random variable defined on the interval 0, 4] with probability density function p(r) e(1 +4) (a) Find the value of c such that p(x) is a valid probability density function b) Find the probability that X is greater than 3 (c) If X is greater than 1, find the probability X is greater than 2 d) What is the probability that X is less than some number a, assuing 0<a<4?
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 X be a continuous random variable defined on the interval [0, 4] with probability density function p(x) = c(1 + 4x) (a) Find the value of c such that p(x) is a valid probability density function. (b) Find the probability that X is greater than 3. (c) If X is greater than 1, find the probability X is greater than 2. (d) What is the probability that X is less than some number a, assuming 0 < a <...
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).
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,...
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.
1. Let X be a continuous random variable with the probability density function fx(x) = 0 35x57, zero elsewhere. Let Y be a Uniform (3, 7) random variable. Suppose that X and Y are independent. Find the probability distribution of W = X+Y.
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...
be a continuous random variable with probability density function 3. Let for 0 r 1 a, for 2 < < 4 0, elsew here 2 7 fx(x) = (a) Find a to make fx(x) an acceptable probability density function. (b) Determine the (cumulative) distribution function F(x) and draw its graph.