Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E (Y)=-5 E(Z)=-1 Var(Y) =1 Var(z)=34 Е (x)--9 Е(Ү)--5 E(z)--1 Compute the values of the expressions below. Е(-5-3х)- О -4Z-4X E -4 Var(-4+Z)= 0 E(-31²)= D Dlo

I'm trying to find the variance of a sample, and I seem to find two different formulas--one involving dividing by n-1, and another by n(n-1).  Attached is the one with the n(n-1) in the formula (disregard the number 30 in the image).     Which one is correct?  My guess is they're both correct.  It's just I don't see what the difference between the two forms is.

Solve completely

20

3. An integer is randomly chosen from the set 1, 2,..., 100. If this integer is divisible by 2 we let Y = 0, and if it is not divisible by 2 but is divisible by 3 then Y = 1. We let Y = 2 in all other cases. Find mean and variance of Y.

Let X be a random variable that can take values x = 2,4,6,8 and has probabilities given by the function P(X = x) = 3x/60 Find (1) P(X = 4) (2) P (X ≤ 6) (3) P(X < 6) (4) P (X ≥ 3)

1. Given that X~N(39,32)A Random variable X is normally distributed and has a mean of 9 C Random variable X is not normally distributed and the mean is 39 B Random variable X is normally distributed and has a mean of 3 D Random variable X is normally distributed and the mean is 39

How do you solve this statistics question without using code? Find P(X1 > X2)

3. An urn contains exactly 10 red chips and 6 blue chips. Five chips are randomly selected without replacement. Let X denote the number of blue chips in the sample of five chips. (a) What type of random variable is X? Indicate both the type and the appropriate parameters using the "~" notation. Write down the pmf of X, and do not forget to indicate the range of values that x can take on. X ~ px (x) (b) What is the probability that there are between two and four blue chips among the five chosen chips? Express your answer as a decimal. = (*)*

Suppose X, Y, and Z are three independent normal random variables. X has an expected value of 7 and a standard deviation of 2; Y has an expected value of -2 and a standard deviation of 4; Z has an expected value of 5 and a standard deviation of 12. Let T = 3X + 12Y - 2Z Variable X Y Mean(Expected Value) 7 -2 Standard Deviation 2 4 12 Coefficient 3 12 -2 a) What is the expected value of T? b) What is the variance of Z? c) What is the variance of T? d) What is the standard deviation of T? N LO