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GATE20 Engg. Mathematics Series: Probability Quiz 3 (App update required to attempt this test)
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Question 1
In any given year, the probability of an earthquake greater than Magnitude 6 occuring in the Garhwal Himalayas is 0.04. The average time between successive occurrences of such earthquakes is ______ years.
Question 2
Out of 800 families with 4 children each, the expected number of families with 2 boys and 2 girls are ________.
Question 3
A packet of 10 bulbs is known to include 2 bulbs that are defective. If 4 bulbs are randomly chosen and tested, the probability of finding among them not more than 1 defective bulb is _________.
Question 4
Consider a dice with the property that the probability of a face with n dots showing up is proportional to n. The probability of the face with three dots showing up is_________.
[write the answer upto two decimal places]
[write the answer upto two decimal places]
Question 5
Let X ϵ {0, 1} be two independent binary random variables. If P(X = 0) = P and P(Y = 0) = q, then P(X + Y ≥ 1) is equal to
Question 6
Consider the following probability mass function (p.m.f) of a random variable X :
If q = 0.4, the variance of X is _______.
If q = 0.4, the variance of X is _______.
Question 7
Let X be a random variable. If E(X)=, Var(X)=, and K is a constant, then
E[(X-K)2] =
E[(X-K)2] =
Question 8
A random variable X has probability density function f(x) as given below.
If the expected value E[X] = 2/3, then Pr[X < 0.5] is
If the expected value E[X] = 2/3, then Pr[X < 0.5] is
Question 9
A fair coin is tossed repeatedly till both head and tail appear at least once. The average number of tosses required will be
Question 10
Let the random variable X represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of X is ______
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