Probability and Statistics Questions and Answers – Mean and Variance of Distribution

This set of Probability and Statistics Multiple Choice Questions & Answers (MCQs) focuses on “Mean and Variance of Distribution”.

1. The expectation of a random variable X (E(X)) can be written as _________
a) \(\frac{d}{dt} [M_X (t)](t=0) \)
b) \(\frac{d}{dx} [M_X (t)](t=0) \)
c) \(\frac{d^2}{dt^2} [M_X (t)](t=0) \)
d) \(\frac{d^2}{dx^2} [M_X (t)](t=0) \)
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2. If the probability of hitting the target is 0.4, find mean and variance.
a) 0.4, 0.24
b) 0.6, 0.24
c) 0.4, 0.16
d) 0.6, 0.16
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3. If the probability that a bomb dropped from a place will strike the target is 60% and if 10 bombs are dropped, find mean and variance?
a) 0.6, 0.24
b) 6, 2.4
c) 0.4, 0.16
d) 4, 1.6
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4. If P(1) = P(3) in Poisson’s distribution, what is the mean?
a) \(\sqrt{2} \)
b) \(\sqrt{3} \)
c) \(\sqrt{6} \)
d) \(\sqrt{7} \)
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5. What is the mean and variance for standard normal distribution?
a) Mean is 0 and variance is 1
b) Mean is 1 and variance is 0
c) Mean is 0 and variance is ∞
d) Mean is ∞ and variance is 0
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6. Find λ in Poisson’s distribution if the probabilities of getting a head in biased coin toss as \(\frac{3}{4} \) and 6 coins are tossed.
a) 3.5
b) 4.5
c) 5.5
d) 6.6
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7. If P(6) = λP(1) in Poisson’s distribution, what is the mean?(Approximate value)
a) 4
b) 6
c) 5
d) 7
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8. Find f(2) in normal distribution if mean is 0 and variance is 1.
a) 0.1468
b) 0.1568
c) 0.1668
d) 0.1768
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9. Find the mean of tossing 8 coins.
a) 2
b) 4
c) 8
d) 1
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10. Mean and variance of Poisson’s distribution is the same.
a) True
b) False
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Sanfoundry Global Education & Learning Series – Probability and Statistics.

To practice all areas of Probability and Statistics, here is complete set of 1000+ Multiple Choice Questions and Answers.

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