1) Suppose X is a Normal RV with mean = 12 and variance = 16. Find...
2) Suppose X is a Normal RV with mean = 17 and variance = 4. Find (a) P(X < 14) (b) P(14.5 < X < 18) (c) P(X < 11 or X > 17) (d) P(X < 11 and X > 17)
3) Suppose X is a Normal RV with mean = 17 and variance = 4. Note this is the same random variable as in Question 2. Find (a) P&717<-1.5) (b) P(-1.25 < *=12 <.5) (c) P(+297 < 2)
1. Using calculus, find the mean and variance of a uniform distribution with a minimum value of of O and a maximum value of 10. (Give a proof.) Remember that the variance can be calculated using: < X z >-< X >2.
(20 points) Suppose X~N(25, 81). That is, X has a normal distribution with μ-25 and σ-81 la. Find a transformation of X that will give it a mean of zero and a variance of one (ie., standardize X lb. Find the probability that 18 < χ < 26. lc. Supposing Y10 +5X, find the mean of Y ld. Find the variance ofY
function, s sin(x) if 0 < x <A otherwise Find the mean and variance of X. Find the mean and variance of the random variable X2 with the fol lowing distributions: - (i) X ~ N(u,0) - (ii) X ~ P(X) - (iii) X ~ Expo(1) "roblem 7 vandam variables,
(20 points) Suppose X-N(25, 81). That is, has a normal distribution with μ-25 and σ2-81. la. Find a transformation of X that will give it a mean of zero and a variance of one (ie., standardize X). lb. Find the probability that 18<x < 26. 1c. Supposing Y = 10 +5X, find the mean of Y 1d. Find the variance of Y
If X is a normal rv with mean 85 and standard deviation 20, compute the following probabilities by standardizing. (a) P(X < 125) .9772 (b) P(X < 85) 5 (c) P(55 SX 125) .9104 (d) P(65 < X) .8413 (e) P(95 <x<115) .2417 (f) P( [X - 850 < 20) .7357
Suppose that Xi are IID normal random variables with mean 2 and variance 1, for i = 1, 2, ..., n. (a) Calculate P(X1 < 2.6), i.e., the probability that the first value collected is less than 2.6. (b) Suppose we collect a sample of size 2, X1 and X2. What is the probability that their sample mean is greater than 3? (c) Again, suppose we collect two samples (n=2), X1 and X2. What is the probability that their sum...
5. Suppose X is a continuous RV modeled by f(x; a) =-e-le-al where-oo < x < 00, If a random sample of size n is drawn with n odd, show the MLE for α is the median of the sample.
Let X = (X1, X2) be a bivariate normal random vector such that Mi = 4,42 = 6,01 = 25, 02 = 16 and p= 0.7. 1. Find P(X2 <5|X1 = 3).