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Gate 2019: Engineering Mathematics Quiz 12 (App update required to attempt this test)
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Question 1
In a housing society, half of the families have a single child per family, while the remaining half has two children per family. The probability that a child picked at random, has a sibling is ___
Question 2
An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is
Question 3
A binary random variable X takes the value of 1 with probability 1/3. X is input to a cascade of 2 independent identical binary symmetric channels (BSCs) each with crossover probability 1/2. The outputs of BSCs are the random variables Y1 and Y2 as shown in the figure.
The value of H(Y1) + H(Y2) in bits is _______.
The value of H(Y1) + H(Y2) in bits is _______.
Question 4
The input to a 1-bit quantizer is a random variable X with pdf 
and 
For outputs to be of equal probability, the quantizer threshold should be _____.
and For outputs to be of equal probability, the quantizer threshold should be _____. Question 5
Consider the Z-channel given in the figure. The input is 0 or 1 with equal probability.
If the output is 0, the probability that the input is also 0 equals ______________
If the output is 0, the probability that the input is also 0 equals ______________
Question 6
Out of 800 families with 4 children each, the expected number of families with 2 boys and 2 girls are _________.
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