{"id":20327,"date":"2024-04-15T05:51:24","date_gmt":"2024-04-15T05:51:24","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=20327"},"modified":"2024-04-15T05:51:24","modified_gmt":"2024-04-15T05:51:24","slug":"x-and-y-are-two-independent-random-variables-with-variances-1-and-2-respectively-let-z-x-y-the-variance-of-z-is-a-0-b-1-c-2-d-3","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/x-and-y-are-two-independent-random-variables-with-variances-1-and-2-respectively-let-z-x-y-the-variance-of-z-is-a-0-b-1-c-2-d-3\/","title":{"rendered":"X and Y are two independent random variables with variances 1 and 2, respectively. Let Z = X – Y. The variance of Z is A. 0 B. 1 C. 2 D. 3"},"content":{"rendered":"

[amp_mcq option1=”0″ option2=”1″ option3=”2″ option4=”3″ correct=”option1″]<\/p>\n

The correct answer is $\\boxed{\\text{B}}$.<\/p>\n

The variance of a random variable is a measure of its spread. It is calculated by taking the square of the standard deviation. The standard deviation is a measure of how far the values of the random variable are from the mean.<\/p>\n

The variance of a sum of two independent random variables is the sum of their variances. This is because the values of the sum are just the sum of the values of the two random variables, so the spread of the sum is just the sum of the spreads of the two random variables.<\/p>\n

In this case, $X$ and $Y$ are two independent random variables with variances 1 and 2, respectively. So, the variance of $Z = X – Y$ is $1 + 2 = \\boxed{3}$.<\/p>\n

Here is a more detailed explanation of each option:<\/p>\n