os the Cdf table of T distribution for different probabilities(p) and different degrees of freedom.
6. Consider a sample X,... X, of normally distributed random variables with mean y and variance...
5. Suppose X is a normally distributed random variable with mean μ and variance 2. Consider a new random variable, W=2X + 3. i. What is E(W)? ii. What is Var(W)? 6. Suppose the random variables X and Y are jointly distributed. Define a new random variable, W=2X+3Y. i. What is Var(W)? ii. What is Var(W) if X and Y are independent?
A random variable X is normally distributed with a mean of 121 and a variance of 121, and a random variable Y is normally distributed with a mean of 150 and a variance of 225. The random variables have a correlation coefficient equal to 0.5. Find the mean and variance of the random variable below. Av-218 (Type an integer or a decimal.) σ (Type an integer or a decimal.)
10. (5pt) Suppose that X and Y are two normally distributed random variables. X has mean 2 and standard deviation !5 Y has mean 5 and standard deviation 3. Their correlation is 0.6. What is the mean and standard deviation of X + Y? What is the distribution of X+ Y? What if X and Y are jointly normally distributed? What if they are not jointly normally distributed? Explain your answer.
4.2.26. Let the random variables X1, X2, ..., X 10 be normally distributed with mean 8 and variance 4. Find a number a such that P(È (= 8)’ sa) = 0.93
Consider a random sample from a normal population with mean u = 3 and variance o2 = 22, with sample size n = 20. Suppose the sample variance is 82 = 2.72. Let p be the probability that s2 exceeds the sample variance 52. Which of the following is true? 0.01 < p < 0.025 0.025 < p < 0.05 0.05<P 0.005< p < 0.01 Op < 0.005
Consider a random sample from a normal population with mean u = 3 and variance o2 = 22, with sample size n = 20. Suppose the sample variance is 82 = 2.72. Let p be the probability that s2 exceeds the sample variance 52. Which of the following is true? 0.01 < p < 0.025 0.025 < p < 0.05 0.05<P 0.005< p < 0.01 Op < 0.005
Consider a random sample from a normal population with mean u = 3 and variance o2 = 22, with sample size n = 20. Suppose the sample variance is 82 = 2.72. Let p be the probability that s2 exceeds the sample variance 52. Which of the following is true? 0.01 < p < 0.025 0.025 < p < 0.05 0.05<P 0.005< p < 0.01 Op < 0.005
Exercise 2. Let consider a normally distributed random variable Z with mean 0 and variance 1. Compute (a) P(Z < 1.34). (b) P(Z > -0.01). (c) the number k such that P(Z <k) = 0.975.
9. The random variable x is distributed normally with mean Mx. and variance 6 and random Variable Y is normally distributed with mean & and Variance or 2x=34 is distributed hormally with mean 12 and variance 42 Assume Independence Find values Ux and by. Possible answers: Mx = 18 & Gyr by=va mx-128 6y=842 My 686y=2 ty=-68
6. (15 pts.) Let X,X.. Xn be independent and identically distributed erponentially distribu random variables, each with mean ux 1. Let a. Calculate E[W] b, Calculate ơw, the variance of W c. Calculate the probability P[X, Ss 1 d. Approximate the probability P[W 1] when n is large e. Suppose n - 1000, and you have one guess at what W is. What numerical value would you pick? What fundamental result in probability theory are you basing your answer on?