Example 20 : If the probability density function of X is given by(x/2,for 0 < x <1|1/2, for 1< x <2f(x) =(3 – x) i 2, for 2 < x<30, elsewhereFind the expected value of f(x) = x – 5x+ 3

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Answered: |Example 20 : If the probability…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Theorem A at Section 8.8.1 saysA necessary and sufficient condition for T(X1,..., Xn) to be sufficient for a parameter θ is that the joint probability function (density function or frequency function) factors in the formf(x1,...,xn|θ) = g[T(x1,...,xn),θ]h(x1,...,xn)
10 - The cumulative probability function is given as follows. Find the Probability density function for a continuous random number 0 <x <6. A) F (x) = 12x +1/2 B) f (x) = (1/36) x +1/2 C) f (x) = (1/36) x +1/12 D) 0 TO) f (x) = (16) x +1/2
suppose that the probability density function of x is f(x)={3x^2, 0, 0<x<1 elsewhere. determine p(x<1/3), P(1/3 <=x<2/3), and P(x=>2/3)
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4 (b) An insurance company provides customers with both auto and home insurance policies. For a particular customer, Χ is the deduction on his or her auto policy and Y is the deduction on the home policy. Possible values of Χ are K100 and K250, and for Y are K0, K100 and K200. The joint probability density function for ( ) ,YΧ is given by the following table: Χ Y K100 K250 K0 0.20 0.05 K100 0.10 0.15 K200 0.20 0.30 iv. If we look only at those insurance customers selecting the lowest auto mobile insurance deduction (K100), what is the probability that a randomly selected\ customer will also select the lowest home deduction (K0). v. Compute the correlation coefficient of Χ and Y
What is the value of the constant c for p(x) to qualify as a probability mass function? ?(?)=?(1/4)x-1 ?? ? = 1, 2, 3, 4, 5, ... and p(x) = 0 otherwise. How would you get c{1-1/4}-1 = 1
Determine E(X), E(X2) and V(X) if X be a continuous random variable with probability density function fx(x) = 3x^2 0 ≤ x ≤ 1 0 otherwise
Verify that p(x) = 3x - 4 is a probability density function on [1, oo)and calculate its mean value.
Q3) The joint probability density function of two discrete random variables X and ¥ is given by p(x, y)=c(2x+3y), where x and can assume all integers such that 0 <
If the joint probability density function of two continuous random variables X and Y isgiven byf(x; y) = 2, 0 < y < 3x, 0 < x < 1; find(a) f(yjx),(b) E(Y jx),(c) Var(Y jx).
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Suppose the joint probability density of X and Y is fX,Y (x, y) = 3y 2 with 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 and zero everywhere else. 1. Compute E[X|Y = y]. 2. Compute E[X3 + X|X < .5]

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|Example 20 : If the probability density function of X is given by (x/2, for 0 < x SI |1/2,for 1< x<2 f(x)= ! (3– x) i 2,for 2 < x<3 0, elsewhere Find the expected value of fx) = x – 5x +3 %3D