# Answer to Question #210105 in Electrical Engineering for Bahawal Tahir

Question #210105

Q9

A student answers a multiple-choice examination question that offers four possible

answers. Suppose the probability that the student knows the answer to the question is

8 and the probability that the student will guess is .2. Assume that if the student

guesses, the probability of selecting the correct answer is .25. If the student correctly

answers a question. what is the probability that the student really knew the correct

Q 10

The probability distribution for a random variable Y is given in table. Find the mean.

variance, and standard deviation of Y .

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2021-06-24T16:46:01-0400

Q9

This is a case of the Bayes theorem

Let B1 denote the event that the student knows the answer

and B2 denote the event that the student guesses the answer

Let A denote the event that the student correctly answer

Given "P(B_1)= 0.8"

"P(B_2)=0.2"

"P(A\/B1)=1"

P(A/B2)= 0.25

We have to find P(B1/A)=

="\\frac{0.8*1}{[0.8*1+0.2*0.25]}"

"=\\frac{0.8}{[0.8+ 0.05]}"

"=\\frac{0.8}{0.85}"

0.9412

Therefore Required Probability is 0.9412

Q10 "Mean, \u03bc = \u01a9[X.P(X)] = 1.2"

Variance "[\u01a9(X\u00b2.P(X)) - \u03bc\u00b2] = (2.2 - 1.2\u00b2)= 0.76"

"Standard \\space deviation, \u03c3 = \\sqrt{[\u01a9(X\u00b2.P(X)) - \u03bc\u00b2]} = \\sqrt{(2.2 - 1.2\u00b2)} = 0.8718"

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