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If a random variable x assumes the values x1 , x2 , x3 , x4 with corresponding probabilities p1 , p2 , p3 , p4 then the expected value of x is
- a)p1 + p2 + p3 + p4
- b)x1 p1 + x2 p3 + x3 p2 + x4 p4
- c)p1 x1 + p2 x2 + p3 x3 + p4 x4
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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If a random variable x assumes the values x1 , x2 , x3 , x4 with corre...
Expected Value of a Random Variable:
The expected value of a random variable is a measure of the central tendency of the distribution of the variable.
It is defined as the weighted average of the values that the variable can take, where the weights are the probabilities of the values.
Expected Value Formula:
The formula for the expected value of a random variable X is:
E(X) = ∑(xi * pi)
where xi is the value that X can take, and pi is the probability of X taking the value xi.
Solution:
Given that the random variable X assumes the values x1, x2, x3, x4 with corresponding probabilities p1, p2, p3, p4.
The expected value of X is given by:
E(X) = ∑(xi * pi)
E(X) = (x1 * p1) + (x2 * p2) + (x3 * p3) + (x4 * p4)
Hence, option (c) is the correct answer.
The expected value of a random variable is a measure of the central tendency of the distribution of the variable.
It is defined as the weighted average of the values that the variable can take, where the weights are the probabilities of the values.
Expected Value Formula:
The formula for the expected value of a random variable X is:
E(X) = ∑(xi * pi)
where xi is the value that X can take, and pi is the probability of X taking the value xi.
Solution:
Given that the random variable X assumes the values x1, x2, x3, x4 with corresponding probabilities p1, p2, p3, p4.
The expected value of X is given by:
E(X) = ∑(xi * pi)
E(X) = (x1 * p1) + (x2 * p2) + (x3 * p3) + (x4 * p4)
Hence, option (c) is the correct answer.
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If a random variable x assumes the values x1 , x2 , x3 , x4 with corresponding probabilities p1 , p2 , p3 , p4 then the expected value of x isa)p1 + p2 + p3 + p4b)x1 p1 + x2 p3 + x3 p2 + x4 p4c)p1 x1 + p2 x2 + p3 x3 + p4 x4d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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