which is the mgf of chi square random variable with 1 df
Prove that if random variable X follows a standard normal distribution (with mean u= 0 and...
Show that if Z is a standard normal random variable then Z2 has the Chi-square distribution with one degree of freedom.
4 Suppose the random variable X follows a normal distribution with mean u = 54and standard deviation o = 10. Calculate each of the following. In each case, round your response to at least 4 decimal places. a) P(X < 42) = Number b) P(X > 61) = Number c) P(49< X < 69) = Number
Given a random variable X follows a Normal distribution with mean 10 and standard deviation 5, what is the probability that X lies within one standard deviation of the mean?
7. Let X a be random variable with probability density function given by -1 < x < 1 fx(x) otherwise (a) Find the mean u and variance o2 of X (b) Derive the moment generating function of X and state the values for which it is defined (c) For the value(s) at which the moment generating function found in part (b) is (are) not defined, what should the moment generating function be defined as? Justify your answer (d) Let X1,...
7. Let Xn Xi++X2, where the Xi's are iid standard normal random variables (a) Show that Sn is a chi-square random variable with n de- grees of freedom. Hint: Show that X is chi-square with one degree of freedom, and then use Problem 6. (b) Find the pdf of (c) Show that T2 is a Rayleigh random variable. (d) Find the pdf for Ts. The random variable Ts is used to model the speed of molecules in a gas. It...
QUESTION 1 A random variable X follows a normal distribution with mean 350 and standard deviation 65. If a sample of size 15 is taken, find P(X> 325). (3 decimal places)
9. (9 pts) The random variable r-Gamma(x-2, β-4). functions to prove that the moment generating function for the random variable W mw(t) (1-12t)2. Use the method of moment-generating 3Y +5is eSt 10, (9 pts) Suppose that Y has a gamma distribution with α-n/2 for some positive integer n and β equal to some specified value. Use the method of moment-generating functions to prove that W- 2Y /g has a Chi-squared distribution with n degrees of freedom. Make sure you show...
If ? is a random variable that follows a normal distribution with a mean of 20 and standard deviation 3.2, what value of ? represents the 50th percentile?
If random variable X has normal distribution with mean u=50 and the standard deviation q=2 , then the value of z-score corresponding to the value X =60 is : - 10 - 5 - 50 - 0
Let X variable Y by be a normal random variable with mean 0 and variance 1. We define the random y2 if x 20, Y= (a For t E R, compute Mr()-Elen'], the moment generating function of Y. Compute EY