1)for this to be valid : f(X) dx = kx2 dx =kx3/3 |2-1 =k(8/3+1/3) =k*3 =1
k=1/3
2)P(|X|>1/2) =P(X<-1/2)+(X>1/2) =x3/9|1/2-1 +x3/9 |21/2 =7/72+7/8 =70/72 =35/36
b. Let X be a continuous random variable with probability density function f(x) = kx2 if...
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.
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 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...
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.
3.98 Let X be a continuous random variable with probability density function f(x) defined on = {xl-π/2 < x < π/2). Give an expression for VIsinX)
(1) Suppose that X is a continuous random variable with probability density function 0<x< 1 f() = (3-X)/4 i<< <3 10 otherwise (a) Compute the mean and variance of X. (b) Compute P(X <3/2). (c) Find the first quartile (25th percentile) for the distribution.
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...
7, Let X be a continuous random variable with probability density function: 0, f x<0 150 f x> 10 ind ihe avnanted value and mode of random variable X
2. Le X be a continuous random variable with the probability density function x+2 18 -2<x<4, zero otherwise. Find the probability distribution of Y-g(X)- XI
Q 2. The probability density function of the continuous random variable X is given by Shell, -<< 0. elsewhere. f(x) = {&e*, -40<3<20 (a) Derive the moment generating function of the continuous random variable X. (b) Use the moment generating function in (a) to find the mean and variance of X.