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Expected value and variance for Gamma and Log-Gamma distribution.
A random variable Y is said to have a log-gamma distribution if X = ln(Y) is a Gamma (alpha, beta) random variable.
Find the E(Y) and the Var(Y). Show all work.
Statistics and Probability, Statistics
A real number between 0 and l00 is randomly selected according to a uniform distribution and rounded off to the nearest integer. For example, 36.5001 is rounded off to 37; √3 is rounded off to 2; and 69.49 is rounded off ...
Write a MATLAB program to generate a Bernoulli process X[n] for which each time instant of the process is a Bernoulli random variable with Pr(X[n]=1) = 0.1 and Pr(X[n]=0) = 0.9 Also, the process is IID (i.e., X[n] is i ...
If the input to a linear filter is a random telegraph process with zero-crossings per second and an amplitude A , determine the output PSD. The filter impulse response is
Let and be independent zero-mean, unit-variance Gaussian random variables. Consider forming the new random variable according to Note that this transformation produces a coordinate rotation through an angle of θ . Find t ...
1. According to the speaker Lionardo, what discourages young men from marrying? 2. What is the main purpose of marriage, according to the characters in the dialogue? 3. In arranging marriages, how much input did the futu ...
A random process X (t ) consists of three-member functions: and Each member function occurs with equal probability. (a) Find the mean function (b) Find the autocorrelation function (c) Is the process WSS? Is it stati ...
Suppose X is a vector of IID random variables where each element has some PDF, Find an example PDF such that the median is a better estimate of the mean than the sample mean.
A gambler plays a game of chance where he wins $1 with probability and loses $1 with probability 1-P each time he plays. The number of games he plays in an hour,N , is a random variable with a geometric PMF (a) What is ...
A random process X(t) has the following member functions: Each member function occurs with equal probability (a) Find the mean function (b) Find the autocorrelation function (c) Is the process WSS? Is it stationary ...
Why do so many women's lives seem to be divided between working for money or goods, and homemaking during the period 1800-1860?
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