Question

5.17 consider the following functions of the random variables Y1, Y2, andY3: W1 = Y1 + Y2 + Y3 W2 = Y1 - Y2 W3 = Y1 - Y2 -Y3 a. state the above in matrix notation b. find the expectation of the random

Answer 1

For a normally distributed random variable Y with a mean (μ) of 2 and a standard deviation (σ) of 1, if y = 4, then the z-score is calculated as z = (4 - 2) / 1, giving a z-score of 2.

Step-by-step explanation:

If we have a normal distribution for the random variable Y given as Y~ N(2, 1), and we know that y = 4, we want to compute the corresponding standard score (z-score). The z-score represents how many standard deviations an element is from the mean. We can calculate the z-score using the formula: z = (y - μ) / σ

Where:

• μ is the mean of the distribution,
• σ is the standard deviation, and
• y is the observed value.

For Y~ N(2, 1), the mean (μ) is 2 and the standard deviation (σ) is 1. Thus:

z = (4 - 2) / 1 = 2 / 1 = 2

Therefore, if y = 4, then the z-score is 2.