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If a random variable x assumes the values 0, 1 and 2 with probabilities 0.30, 0.50 and 0.20, then its expected value is
- a)1.50
- b)3
- c)0.90
- d)1
Correct answer is option 'C'. Can you explain this answer?
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If a random variable x assumes the values 0, 1 and 2 with probabilitie...
Expected Value of a Random Variable:
The expected value of a random variable is the sum of the product of each possible value of the variable and its probability.
Formula:
E(X) = Σ(x × P(X=x))
where E(X) is the expected value of the random variable X, x is the possible value of X, and P(X=x) is the probability that X takes the value x.
Solution:
Given, a random variable x assumes the values 0, 1, and 2 with probabilities 0.30, 0.50, and 0.20 respectively.
Using the formula of expected value, we have
E(X) = Σ(x × P(X=x))
= 0 × 0.30 + 1 × 0.50 + 2 × 0.20
= 0 + 0.50 + 0.40
= 0.90
Therefore, the expected value of the random variable X is 0.90.
Hence, option (c) is the correct answer.
The expected value of a random variable is the sum of the product of each possible value of the variable and its probability.
Formula:
E(X) = Σ(x × P(X=x))
where E(X) is the expected value of the random variable X, x is the possible value of X, and P(X=x) is the probability that X takes the value x.
Solution:
Given, a random variable x assumes the values 0, 1, and 2 with probabilities 0.30, 0.50, and 0.20 respectively.
Using the formula of expected value, we have
E(X) = Σ(x × P(X=x))
= 0 × 0.30 + 1 × 0.50 + 2 × 0.20
= 0 + 0.50 + 0.40
= 0.90
Therefore, the expected value of the random variable X is 0.90.
Hence, option (c) is the correct answer.
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If a random variable x assumes the values 0, 1 and 2 with probabilities 0.30, 0.50 and 0.20, then its expected value isa)1.50b)3c)0.90d)1Correct answer is option 'C'. Can you explain this answer?
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