GATE exam stream
174 questions and papers
Suppose \(X_i\) for \(i=1,2,3\) are independent and identically distributed random variables whose probability mass functions are \(\Pr[X_i=0]=\Pr[X_i=1]=1/2\) for \(i=1,2,3\). Define another random variable \(Y=X_1X_2\oplus X_3\), where \(\oplus\) denotes XOR. Then…
Four fair six-sided dice are rolled. The probability of the sum of the results being 22 is \(\dfrac{X}{1296}\). The value of \(X\) is ______.
Suppose \(p\) is 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…
Consider a random variable \(X\) that takes values \(+1\) and \(-1\) with probability \(0.5\) each. The values of the cumulative distribution function \(F(x)\) at \(x=-1\) and \(x=+1\) are
Consider a company that assembles computers. The probability of a faulty assembly of any computer is \(p\). The company therefore subjects each computer to a testing process. This…
An unbalanced die (with 6 faces, numbered from 1 to 6) is thrown. The probability that the face value is odd is \(90\%\) of the probability that the face value is even. The probability of getting any even numbered face is the same. If the probability that the face is even given that it is greater than 3 is \(0.75\), which one of the following…
For each element in a set of size \(2n\), an unbiased coin is tossed. The \(2n\) coin tosses are independent. An element is chosen if the corresponding coin…
Aishwarya studies either computer science or mathematics every day. If she studies computer science on a day, then the probability that she studies mathematics the next day is…
An examination paper has 150 multiple-choice questions of one mark each, with each question having four choices. Each incorrect answer fetches \(-0.25\) marks. Suppose 1000 students choose all…
Consider a process executing on an operating system that uses demand paging. The average time for a memory access in the system is \(M\) units if the corresponding…
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