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In a meeting, 60% of the members favour and 40% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Find E(X) and Var(X).
- a)0.6 and 0
- b)0.6 and 0.44
- c)0.6 and 0.24
- d)0.4 and 0.24
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
In a meeting, 60% of the members favour and 40% oppose a certain propo...
Solution:
Given,
P(X=1) = 0.6, P(X=0) = 0.4
We know that,
E(X) = ΣxP(x)
So,
E(X) = (0 × 0.4) + (1 × 0.6)
E(X) = 0.6
Now, we need to find the variance of X, which can be calculated as follows:
Var(X) = E(X^2) - [E(X)]^2
We know that,
E(X^2) = Σx^2P(x)
So,
E(X^2) = (0^2 × 0.4) + (1^2 × 0.6)
E(X^2) = 0.6
Therefore,
Var(X) = 0.6 - (0.6)^2
Var(X) = 0.24
Hence, the correct answer is option C, i.e., 0.6 and 0.24.
Given,
P(X=1) = 0.6, P(X=0) = 0.4
We know that,
E(X) = ΣxP(x)
So,
E(X) = (0 × 0.4) + (1 × 0.6)
E(X) = 0.6
Now, we need to find the variance of X, which can be calculated as follows:
Var(X) = E(X^2) - [E(X)]^2
We know that,
E(X^2) = Σx^2P(x)
So,
E(X^2) = (0^2 × 0.4) + (1^2 × 0.6)
E(X^2) = 0.6
Therefore,
Var(X) = 0.6 - (0.6)^2
Var(X) = 0.24
Hence, the correct answer is option C, i.e., 0.6 and 0.24.
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Community Answer
In a meeting, 60% of the members favour and 40% oppose a certain propo...
Odds in favor p=3/5
odds in opposition q=2/5
no of selections n=1
mean in E{x}= np
and variance is V{x}=npq
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In a meeting, 60% of the members favour and 40% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Find E(X) and Var(X).a)0.6 and 0b)0.6 and 0.44c)0.6 and 0.24d)0.4 and 0.24Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a meeting, 60% of the members favour and 40% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Find E(X) and Var(X).a)0.6 and 0b)0.6 and 0.44c)0.6 and 0.24d)0.4 and 0.24Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a meeting, 60% of the members favour and 40% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Find E(X) and Var(X).a)0.6 and 0b)0.6 and 0.44c)0.6 and 0.24d)0.4 and 0.24Correct answer is option 'C'. Can you explain this answer?.
In a meeting, 60% of the members favour and 40% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Find E(X) and Var(X).a)0.6 and 0b)0.6 and 0.44c)0.6 and 0.24d)0.4 and 0.24Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a meeting, 60% of the members favour and 40% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Find E(X) and Var(X).a)0.6 and 0b)0.6 and 0.44c)0.6 and 0.24d)0.4 and 0.24Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a meeting, 60% of the members favour and 40% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Find E(X) and Var(X).a)0.6 and 0b)0.6 and 0.44c)0.6 and 0.24d)0.4 and 0.24Correct answer is option 'C'. Can you explain this answer?.
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