Test: Probability and Statistics - 3 - Mathematics MCQ

The last three digits of a telephone number have been erased and all we know is that the number was 25785???. Assuming that all possibilities are equally likely, the probability that the missing digits are all equal to each other is

If the letters of the word REGULATION' be arranged at random, the probability that there will be exactly 4 letters between R and E is

You have three coins in your pocket, two fair ones but the third biased with probability of heads p and tails 1 - p. One coin selected at random drops to the floor, landing heads up. How likely is it that it is one of the fair coins?

If A ∩ B = φ and B ∩ C = φ, then P(A∪B∪C) = 

A point P is chosen at random on a line AB of length 2l. The probability P[(AP x BP) > R/2] is

An ordinary deck of 52 playing cards is randomly divided into 4 piles of 13 cards each. The probability that each pile has exactly 1 ace is 

An infinite sequence of independent trials is to bo performed. Each Trial results in success with probability p and a failure with probability 1 - p. What is the probability that at least one success occurs in the first n trials?

Two towns A and B are 60 km apart. A school is to be built, to serve 150 students from town A and 50 students from town B. If the total distance travelled by all 200 students is to be as small as possible, then the school should be built at

A random variate has the following distribution:

The value of k is

The voltage across a register is a random variable E uniform between 5V and 10 V. given the resistance of the register R = 1000 Ω, the probability density function of the power W = E²/R dissipated in R is

A random variate X has the following p.m.f. 
 j = 0, 1, 2,...
0 < p < 1
for any two positive integers m and n P(X > m + n | X > m) equals

If an m / m / 1 queue, the inter-arrival time distribution is

Suppose that the number of typographical errors on a single page of a certain book has a Poisson distribution with parameter λ = 1/2. In 600 pages book, the average number of errors in the book is

If X₁ and X₂ are independent normal random variables with parameters  respectively then X₁ - X₂ is normal with mean μ and variance σ² such that

Let λ be a constant. Then var (λ X) = k var X, where k equals 

The weighted arithmetic mean of the first n natural numbers whose weights are equal to the corresponding numbers is given by

In a bivariate distribution, the lines of regression are 3x - 4y = 1 and x + y = 0, then the correlation coefficient r_xy is