AP EAMCET · Maths · Probability

The discrete random variables $X$ and $Y$ are independent from one another and are defined as $X ~ B (16, 0.25)$ and $Y ~ P (2)$ . Then the sum of the variances of $X$ and $Y$ is

A $4$
B $5$
C $6$
D $2$

Verified Solution

Answer & Solution

Correct Answer

(B) $5$

Step-by-step Solution

Detailed explanation

Given, The discrete random variables X and Y are independent from one another and are defined as X~B16,0.25 and Y~P2, Now given for X, n=16 and p=0.25, so q=1-0.25=0.75, Now variance is given by npq=16×0.25×0.75=3 And variance of Y is given as 2, So sum of…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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The discrete random variables X and Y are independent from one another and are defined as X~B16,0.25 and Y~P2. Then the sum of the variances of X and Y is

Step-by-step Solution

The discrete random variables $X$ and $Y$ are independent from one another and are defined as $X ~ B (16, 0.25)$ and $Y ~ P (2)$ . Then the sum of the variances of $X$ and $Y$ is