MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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- 5. Test whether the following expression is a valid pdf. If it is a valid pdf, obtain the CDF and its mean. 1 X 2x +) = -— exp( - ² ) + ²/12/² g(x)= X (+).x20 -exparrow_forwardX1,X2,...,Xn are i.i.d. random variables from N(0,θ) distribution. Here, θ= σ2 >0is the variance of the distribution, and is an unknown parameter. Find the MLE of θ(no need tocalculate the second derivative).arrow_forwardThe moment generating function can be used to find the mean and variance of the normal distribution. Use derivatives of Mx(t) to verify that E(X) = µ and V(X) = 0².arrow_forward
- Suppose X and Y are two independent variables with variance 1. Let Z = X+bY where b > 0. If Cor(Z, Y ) = 1/2, what is the value of b?arrow_forwardQ5 Find the variance for the PDF px(x) = e-«/2, x > 0.arrow_forward3. 1 + x Check whether the following function is a valid pdf? If it is valid, obtain its CDF. If not valid, would scaling by a constant make it valid? If so, make it valid. Obtain its CDF? What is its mean? Variance? ƒ = —exp(-√x)U(x)arrow_forward
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