This set of Probability and Statistics Multiple Choice Questions & Answers (MCQs) focuses on "Mathematical Expectation".

1. The expectation of a random variable X(continuous or discrete) is given by _________

a) xf(x), xf(x)

b) x2f(x), x2f(x)

c) f(x), f(x)

d) xf(x2), xf(x2)

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2. Mean of a random variable X is given by _________

a) E(X)

b) E(X2)

c) E(X2) - (E(X))2

d) (E(X))2

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3. Variance of a random variable X is given by _________

a) E(X)

b) E(X2)

c) E(X2) - (E(X))2

d) (E(X))2

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4. Mean of a constant 'a' is ___________

a) 0

b) a

c) a/2

d) 1

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5. Variance of a constant 'a' is _________

a) 0

b) a

c) a/2

d) 1

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6. Find the mean and variance of X?

x01234f(x)1/92/93/92/91/9

a) 2, 4/3

b) 3, 4/3

c) 2, 2/3

d) 3, 2/3

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7. Find the expectation of a random variable X?

x0123f(x)1/62/62/61/6

a) 0.5

b) 1.5

c) 2.5

d) 3.5

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8. Find the expectation of a random variable X if f(x) = ke-xfor x>0 and 0 otherwise.

a) 0

b) 1

c) 2

d) 3

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9. Find the mean of a random variable X if f(x) = x -52for 0

a) 3.5

b) 3.75

c) 2.5

d) 2.75

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10. Find the mean of a continuous random variable X if f(x) = 2e-xfor x>0 and -exfor x<0.

a) 0

b) 1

c) 2

d) 3