4. (10pt) Prove Ỳ, the vector of fitted values, is normally distributed with mean XB and variance oʻX(X'X)-'X'.
4. If the random variable X is normally distributed with mean = 4 and variance o2 = 2, find the values 2o such that a.) P(SX 330) = 0.4770 b.) PICOS X < 5) = 0.3770
If X is Normally distributed with a mean of 3 and a variance of 4, find P(|X−3|>1.6) to 2 decimal places. The probability is:
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
Problem 4. Let X be normally distributed with mean 1 and variance 2.2. (a) Find P0.5 < X < 2). (b) Find 95th percentile of X.
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.)
How to prove a Brownian Motion Process {X(t),t>=o} that its X(t) is normally distributed with mean 0 and variance σ2t using Central Limit Theorem?
prove that -slly distributed with mean- O and variance - 1, regardless ofthe particular values ofs and
6. Consider a sample X,... X, of normally distributed random variables with mean y and variance op. Let 5 be the sample variance and suppose that n = 16. What is the value of c for which p[x - SS (C2 - 1)] = 95 ? be the 7. Consider a sample X,...,X, of normally distributed random variables with variance o? = 30. Let S sample variance and suppose that n-61. What is the value of c for which P...
Let X be normally distributed with mean 95 and variance 74. Find the variance of -3.2 + 0.7X. a. none of the answers provided here b. 51.8 c. 36.3 d. 2.8 e. 33.1
4. Suppose X1, . . . ,X, are independent, normally distributed with mean E(Xi) and variance Var(X)-σί. Let Żi-(X,-μ.)/oi so that Zi , . . . , Ζ,, are independent and each has a N(0, 1) distribution. Show that LZhas a x2 distribution. Hint: Use the fact that each Z has a xî distribution i naS