ActivityShow that each of the following is a probability mass function11.x, ifx€{1, 2}P(X=x)={310,otherwise.2.1', if x € {1, 2, 3, 4, 5}P(X = x)={55%3D%3D0,otherwise.

In statistics, the continuous variables are variables whose values can be given by an interval, they…

Answered: Show that each of the following is a…

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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Q.3 The probability density function for a continuous random variable X is fx (x) = {"* Sa+ bx2; 0< x< 1, 0; %3D е. w. (i) Find constants a and b if E(X) = 0.6 (ii) Find cumulative distribution function (cdf), moment generating function. (iii) Using mgf, find B1 and Bß2 and comment on it. (iv) Sketch pdf and cdf.
Could you please help with 3(c), 3(d) and 3(e). Thanks
Please solve asap.
4 If X has the probability density function fx(x) %3D еxp (-х), х> 0 0 = Find the expected value of g(X)= exp (3x/4) otherwise %3D
2. Assume X,~N (µ,o²). Let T=(1/n)E(x, -x)', T; = (1/(n – 1))E(x, -x)'. %3D 2 Find the expected value of each above function.
Assume that you have random variable X with the following probability density function with a > 0, b > 0: Г(а+) I(a)T(b) (1 – x)b-1 if € (0, 1) -1 fx(x) = otherwise. (a) Suppose that a = 2 and b = 2. In this case, derive E[X] and var[X]. (b) Continuing with the X from part (a) with a = 2 and b = 2, let Z|X = x ~ Binomial(n, x). Find E[Z] and var[Z]. (c) Find the probability density function of Y defined by the following transfor- mation: Y = 1— Х
please answer number 1
Solve both parts
1. Suppose that for a certain life the probability density function is x (*) 1+x ,x >0 X. Find (i) the survival function ofx (ii) the probability that the life aged 25 will die within next 15 years. (iii) the probability that the life aged 42 will die between 55 and 62.
please answer number 3
15. A random variable X has probability density function 2x, 0 0.75 /X > 0.5).

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Show that each of the following is a probability mass function 1. x, ifx €{1, 2} P(X = x)={3 0, %3D otherwise. 1 x', if x € {1, 2, 3, 4, 5} P(X = x)={55 %3D 0, otherwise. 2.