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A continuous random variable, X is distributed in interval 0 – 10. The probability, P(x = 2) is ______
Correct answer is '0'. Can you explain this answer?
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A continuous random variable, X is distributed in interval 0 – 1...
In case of continuous random variable probability at a point = 0
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A continuous random variable, X is distributed in interval 0 – 1...
1. The probability density function of X is given by:
f(x) = 2x (0 < x="" />< />
2. The cumulative distribution function of X is given by:
F(x) = x^2 (0 < x="" />< />
3. The expected value of X is given by:
E(X) = ∫0^1 x*f(x) dx = ∫0^1 2x^2 dx = 2/3
4. The variance of X is given by:
Var(X) = E(X^2) - [E(X)]^2
E(X^2) = ∫0^1 x^2*f(x) dx = ∫0^1 2x^3 dx = 1/2
Therefore, Var(X) = 1/2 - (2/3)^2 = 1/18
f(x) = 2x (0 < x="" />< />
2. The cumulative distribution function of X is given by:
F(x) = x^2 (0 < x="" />< />
3. The expected value of X is given by:
E(X) = ∫0^1 x*f(x) dx = ∫0^1 2x^2 dx = 2/3
4. The variance of X is given by:
Var(X) = E(X^2) - [E(X)]^2
E(X^2) = ∫0^1 x^2*f(x) dx = ∫0^1 2x^3 dx = 1/2
Therefore, Var(X) = 1/2 - (2/3)^2 = 1/18
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A continuous random variable, X is distributed in interval 0 – 10. The probability, P(x = 2) is ______Correct answer is '0'. Can you explain this answer?
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