Probability-and-statistics Questions Set 2:
If A ⊆ B and B ⊆ A, then
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If A and B are two mutually exclusive events with P(~A) = 5/6 and P(B) = 1/3, then P(A|~B) is equal to
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4 coins are tossed 100 times, and the following results were obtained. What is the mean number of heads?
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If X and Y are two independent random variables, what is the expected value of their product, E(X·Y)?
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In a binomial distribution, the skewness is positive when the probability of success, p, is:
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A fair coin is tossed independently 4 times. The probability of the event 'Number of tails shown up is more than number of heads shown up' is
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If the covariance between variables X and Y is 45, and the variances of X and Y are 49 and 64 respectively, find the coefficient of correlation.
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Let A and B be two events such that the occurrence of A implies the occurrence of B, but not vice-versa. What is the correct relation between P(A) and P(B)?
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Let P be the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and P has a Poisson distribution with a mean of 3. What is the probability of observing fewer than 3 cars during any given minute in this interval?
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A company's system was hacked and it lost a huge amount of data. They were able to recover some correlation data:
Regression Equations: 8X - 10Y + 66 = 0
40X - 18Y = 214
Using these recovered data, find the mean values of X and Y.
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