Question

Let X be a random variable with density f X ( x ) = ( 1...

Let X be a random variable with density f X ( x ) = ( 1 / 2 ) cos ⁡ x for x ∈ [ − π / 2 , π / 2 ]. (a) Show that this is a valid density function. (b) What is the distribution function of Y = sin ⁡ X? (c) What is the density function of Y?

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let X be a random variable with probability density function given by f(x) = 2(1 −...
Let X be a random variable with probability density function given by f(x) = 2(1 − x), 0 ≤ x ≤ 1,   0, elsewhere. (a) Find the density function of Y = 1 − 2X, and find E[Y ] and Var[Y ] by using the derived density function. (b) Find E[Y ] and Var[Y ] by the properties of the expectation and the varianc
Let X be a random variable with density function f(x) = 1/4 for -3 <= x...
Let X be a random variable with density function f(x) = 1/4 for -3 <= x <= 5, and 0 otherwise. Find the density of Y = X^2 and of Y = (X - 1)^2, of Y = |X-1|, and of Y=(X-1)^4.
Let (X, Y) be a random vector (or a random variable) with joint density f (X,...
Let (X, Y) be a random vector (or a random variable) with joint density f (X, Y) (x, y) = 3 (x + y)1(0,1) (x + y)1(0,1) (x)1(0.1) (y), with 1 (0,1) = indicator function. a) Calculate the marginal density functions of X and Y, respectively. b) Calculate the conditional density functions of X given Y = y, and of Y given X = x. c) Are X and Y independent?
Consider a continuous random variable X with the probability density function f X ( x )...
Consider a continuous random variable X with the probability density function f X ( x ) = |x|/C , – 2 ≤ x ≤ 1, zero elsewhere. a) Find the value of C that makes f X ( x ) a valid probability density function. b) Find the cumulative distribution function of X, F X ( x ).
Let X be a continuous random variable with the probability density function f(x) = C x,...
Let X be a continuous random variable with the probability density function f(x) = C x, 6 ≤ x ≤ 25, zero otherwise. a. Find the value of C that would make f(x) a valid probability density function. Enter a fraction (e.g. 2/5): C = b. Find the probability P(X > 16). Give your answer to 4 decimal places. c. Find the mean of the probability distribution of X. Give your answer to 4 decimal places. d. Find the median...
Let X be a random variable with density function f(x) = 2 5 x for x...
Let X be a random variable with density function f(x) = 2 5 x for x ∈ [2, 3] and f(x) = 0, otherwise. (a) (6 pts) Compute E[(X − 2)3 ] without attempting to find the density function of Y = (X − 2)3 . (b) (6 pts) Find the density function of Y = (X − 2)3
1 (a) Let f(x) be the probability density function of a continuous random variable X defined...
1 (a) Let f(x) be the probability density function of a continuous random variable X defined by f(x) = b(1 - x2), -1 < x < 1, for some constant b. Determine the value of b. 1 (b) Find the distribution function F(x) of X . Enter the value of F(0.5) as the answer to this question.
Let X be a random variable with probability density function f(x) = { λe^(−λx) 0 ≤...
Let X be a random variable with probability density function f(x) = { λe^(−λx) 0 ≤ x < ∞ 0 otherwise } for some λ > 0. a. Compute the cumulative distribution function F(x), where F(x) = Prob(X < x) viewed as a function of x. b. The α-percentile of a random variable is the number mα such that F(mα) = α, where α ∈ (0, 1). Compute the α-percentile of the random variable X. The value of mα will...
Let the probability density function of the random variable X be f(x) = { e ^2x...
Let the probability density function of the random variable X be f(x) = { e ^2x if x ≤ 0 ;1 /x ^2 if x ≥ 2 ; 0 otherwise} Find the cumulative distribution function (cdf) of X.
A continuous random variable X has the following probability density function F(x) = cx^3, 0<x<2 and...
A continuous random variable X has the following probability density function F(x) = cx^3, 0<x<2 and 0 otherwise (a) Find the value c such that f(x) is indeed a density function. (b) Write out the cumulative distribution function of X. (c) P(1 < X < 3) =? (d) Write out the mean and variance of X. (e) Let Y be another continuous random variable such that  when 0 < X < 2, and 0 otherwise. Calculate the mean of Y.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT