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GATE 2020 : Engg. Mathematics Quiz 6

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Question 1

If the proportion of handicapped people in a large population is 0.006, then what is the probability that there will be atmost one handicapped person in a randomly chosen group of 500 people. Use poisson approximation to compute the probability.

Question 2

Match the following Lists.
List-I
A-

B-

C-

D-

List-II
1- Discrete distribution
2- Continuous distribution

Question 3

Let X be a random variable following normal distribution with mean +1 and variance 4. Let Y be another normal variable with mean –1 and variance unknown. If P(X ≤ -1) = P(Y ≥ 2), the standard deviation of Y is

Question 4

Let X be the random variable. Consider the following table with the probability distribution values of X.

Find the value of P(X<4).Round upto two decimal places).

Question 5

Let X be a random variable following normal distribution with mean +1 and variance 4. Let Y be another normal variable with mean -1 and variance unknown. If P(X≤ -1) = P(Y ≥ 2), the standard deviation of Y is

Question 6

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 =X₁X₂⊕X₃, where ⊕ denotes XOR. Then Pr^[Y=0^|X₃=0^] = _____________.

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