Question

Let X and Y be jointly normal random variables with parameters $\mu_x = 0$, $\sigma_x^2 = 1$ and $\mu_y = -1$, $\sigma_y^2 = 4$ and $\rho = -1/2$. Using the normal cdf table: (a) Find $P(X + Y > 0)$ (5 pts) (b) Find the constant a if we know $aX + Y$ and $X + 2Y$ are independent. (10 pts) (c) Find $P(X + Y > 0|X + Y > -3)$. You can use normal cdf tables. (10 pts)

          Let X and Y be jointly normal random variables with parameters $\mu_x = 0$, $\sigma_x^2 = 1$ and $\mu_y = -1$, $\sigma_y^2 = 4$ and $\rho = -1/2$. Using the normal cdf table:
(a) Find $P(X + Y > 0)$ (5 pts)
(b) Find the constant a if we know $aX + Y$ and $X + 2Y$ are independent. (10 pts)
(c) Find $P(X + Y > 0|X + Y > -3)$. You can use normal cdf tables. (10 pts)

Let X and Y be jointly normal random variables with parameters = 0, ^2 = 1 and = -1, ^2 = 4 and ρ = -1/2. Using the normal cdf table:
(a) Find P(X + Y > 0) (5 pts)
(b) Find the constant a if we know aX + Y and X + 2Y are independent. (10 pts)
(c) Find P(X + Y > 0|X + Y > -3). You can use normal cdf tables. (10 pts)

Added by Travis S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

04/30/2022

Step 1

The mean of the sum is the sum of the means, and the variance of the sum is the sum of the variances plus twice the covariance. Mean of X + Y = 0 + (-1) = -1 Variance of X + Y = 1 + 4 + 2(-1/2) = 5 Show more…

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Let X and Y be jointly normal random variables with parameters x = 0, ox = 1 and y = -1, oy = 4 and = -1/2. Using the normal cdf table: (a) Find P(X + Y > 0) (5 pts) (b) Find the constant a if we know aX + Y and X + 2Y are independent. (10 pts) (c) Find P(X + Y > 0|X + Y > -3). You can use normal cdf tables. (10 pts