X is a random variable with exponential distribution whose expectation is . Prove :
Let X is a random variable with exponential distribution whose expectation is
The pdf of X is
The required expectation is
But for an integer k>0 (that is when k=1,2,3...) the Gamma function is
and hence the expectation is
X is a random variable with exponential distribution whose expectation is . Prove : We were...
1. Let X be a discrete random variable with a cumulative distribution function: a. Use this cdf to fin the limiting distribution of the random variable when with , as n increases. Use the fact b. What kind of random variable is for large value of n? We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imagep= We were unable to transcribe this imageWe were unable to transcribe this imageWe were...
Let X ~ Poisson(). Show that as , converges in distribution to a random variable Y and find the distribution of Y. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Define a random variable , and a new random variable Y, such that 1) Find the density function of Y.( Instruction: Find the the cumulative distribution function and the derivative it) 2) Find the expectation of Y for (Hint: look for its connection with normal distribution of random variable) T~erp(A) We were unable to transcribe this imageWe were unable to transcribe this image
Let X be a random variable from a distribution with density . Calculate the variance of random variable We were unable to transcribe this image3.22 +1
Continuous random variable X has pdf for , where is symmetric about x = 0. Evaluate where is the cumulative distribution function of X and k > 0. fr) We were unable to transcribe this imagefr) We were unable to transcribe this imageFr(r
Suppose is a random sample from exponential distribution having unknown mean . We wish to test vs. . Consider the following tests: Test 1: Reject if and only if ; Test 2: Reject if and only if Find the power of each test at . We were unable to transcribe this imageWe were unable to transcribe this imageHo : θ = 4 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this...
exponential distribution 3. The distribution of Smith's future lifetime is X, an exponential random variable with mean a, and the distribution of Brown's future lifetime is Y, an exponential random variable with mean B. Smith and Brown have future lifetimes that are independent of one another. Find the probability that Smith outlives Brown. Answer #3: (D) a (E) (A) (B) (C) 3. The distribution of Smith's future lifetime is X, an exponential random variable with mean a, and the distribution...
5.26!!! please T oni Variable when the expectation exists. In the mou having an exponential distribution with population mean 1/2. ity function of the random variable X. 5.26 If E[X" =n! for n=1,2,..., find the probability density function of the ran 627 The lifetime of a narticular light bulb follows an exponential distribution. If the populatie
A random variable X obeys the exponential distribution law xp-x),(20). m! Prove that the following inequality holds true: