and another random variable Y = 2X. Then find (a) value K, (b) E[X], (c) E[Y] and (d) E[XY].
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![Consider that a pdf of a random variable X is
1
-25x53
fx (x)
={K
otherwise
and another random variable Y = 2X. Then find (a) value K, (b) E[X], (c) E[Y] and
( d) EΧΥ.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4102b207-3d31-4615-92c2-8465f48d05c9%2Fd95c857c-9f32-43c5-bc47-9f6ad495420b%2F764aven_processed.jpeg&w=3840&q=75)
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.X is an exponential random variable with λ =1 and Y is a uniform random variable defined on (0, 2). If X and Y are independent, find the PDF of Z = X-Y2Find the variance by calculating the first two moments of the random variable X = (- 1 / λ) ln (1-U), where U ~ U (0,1) and λ> 0.
- We have a random variable X and Y that have the joint pdf f(x) = {1 0<x<1, 0<y<1} {0 otherwise} If U = Y-X2 , what would the pdf of the random variable U be? What is the support for the random variable U? Would there be any critical points? (use CDF technique)If Y is a continuous, uniformly distributed random variable over the interval(4,10), then the value of the PDF between 4 and 10 is?Consider a function F (x ) = 0, if x < 0 F (x ) = 1 − e^(−x) , if x ≥ 0 Is the corresponding random variable continuous?
- Let X be a Gaussian random variable (0,1). Let M = ln(5*X) be a derived random variable. What is E[M]?Let X be a random variable with pdff(x) = 4x^3 if 0 < x < 1 and zero otherwise. Use thecumulative (CDF) technique to determine the pdf of each of the following random variables: 1) Y=X^4, 2) W=e^(-x) 3) Z=1-e^(-x) 4) U=X(1-X)If X is a random variable that is uniformly distributed between -1 to 1, find the PDF √|X| of and pdf of -ln|X|
- Use the moment generating function technique to solve. Let X1, . . . , Xn be independent random variables, such that Xi ∼ Exponential(θ), for i =1, . . . , n. Find the distribution of Y = X1 + · · · + Xn.A continuous random variable X has a pdf of the form: f(x) = (824/9) x^2, for 0.01 < X < 0.32. Calculate the standard deviation (sigma) of X.Consider random variables X and Y with the joint PDF below find pxy
