A random variable X is known to always be positive and have a standard deviation of 5 and E[x^2] = 125. Another random variable (Y) is known to have a mean twice as large as (X) and E[Y^2] = 500. Find the following:
a.) E[X]
b.) E[2X + 5]
c.) Var(Y)
d.) E[(Y-5)^2]
e.) Assuming X and Y are independent find Var(2X - Y +5)
A random variable X is known to always be positive and have a standard deviation of...
If X is a random variable with mean -3 and standard deviation 2, Y is a random variable with mean 5 and standard deviation 3, and the correlation between X and Y is ρ Corr(X, Y) = .8, find Cov(2x-Y, X + 5Y). If X is a random variable with mean -3 and standard deviation 2, Y is a random variable with mean 5 and standard deviation 3, and the correlation between X and Y is ρ Corr(X, Y) =...
4. Standard deviation and risk. The standard deviation o(X) of a random variable is the square root of the variance that is o(X) = Var(X). It characterizes the "spread" of the random variable X. If a random variable X has expected value p and standard deviation o, then X takes values which are on average at distance o from u. Imagine you have the choice to invest in two stock funds: an American fund with a rate return X and...
A random variable X has an expected value of 10 with a standard deviation of 5. Let Y= 5 -2*X be another random variable. Find the expected value of Y and its standard deviation
Let a random variable X be uniformly distributed between −1 and 2. Let another random variable Y be normally distributed with mean −8 and standard deviation 3. Also, let V = 22+X and W = 13+X −2Y . (a) Is X discrete or continuous? Draw and explain. (b) Is Y discrete or continuous? Draw and explain. (c) Find the following probabilities. (i) The probability that X is less than 2. (ii) P(X > 0) (iii) P(Y > −11) (iv) P...
The random variable x has a normal distribution with standard deviation 2525. It is known that the probability that x exceeds 159159 is .90. Find the mean μ of the probability distribution.
The random variable x has a normal distribution with standard deviation 24.It is known that the probability that x exceeds 170 is .90. Find the mean μ of the probability distribution.
Questionl The random variable X and Y have the following joint probability mass function: 0.14 0.27 0.2 0.1 0.03 0.15 0.1 a) Determine the b) Find P(X-Y>2). c) Find PX s3|Y20) d) Determine E(XY) e) Determine E(X) and E(Y). f) Are X and Y independent? marginal pmf for X and Y. Question 2 Let X and Y be independent random variables with pdf 2-y 0sxS 2 f(x)- f(p)- 0, otherwise 0, otherwise a) b) Find E(XY). Find Var (2X +...
Suppose x is a normal random variable with mean u and standard deviation o. If z is the standardized normal random variable of x, which of the following statements is false? (1) When r = y, the value of z=0. (2) When z is less than the mean y, the value of z is negative. (3) When r is greater than the mean y, the value of z is positive. (4) It is always the case that z <I.
(c) The standard deviation of X must always be positive. (d) Adding a constant to a random variable does not effect the standard deviation
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?