Engineering Mat...

If a random variable has a Poisson distribution such that P(1) = P(2), find the mean of the distribution.

Given the equation of line of regression of x on y, determine its regression coefficient.

\(x - \bar x = \frac{{r{\sigma _x}}}{{{\sigma _y}}}\left( {y - \bar y} \right)\;\)

Questions are asked to Girish in quiz competition one by one until be fails to answer correctly. The probability of his answering correctly a question is P. The probability that he will quit after answering on odd number of questions is 0.9. The value of P is

Suppose there is a disease, whose average incidence is 2 per million people. What is the probability that a city of 1 million people has at least twice the average incidence? (Assume Poisson distribution parameter is 2)

The average number of defects per wafer (defect density) is 3. The redundancy into the design allows for up to 4 defects per wafer. What is the probability that the redundancy will not be sufficient if the defects follow a Poisson distribution?

Let X and Y be the time (in hours) taken by Saurabh and Sachin to solve a problem. Suppose that each of X and y are uniformly distributed over the interval [0, 1]. Assume that Saurabh and Sachin start to solve the problem independently. Then, the probability that the problem will be solved in less than 20 minutes is 

Consider the following regression equations obtained from a correlation table:

Y = 0.516 x + 33.73

x = 0.512y + 32.52

A missile can successfully hit a target with probability 0.75. If three successful hits can destroy the target completely, how many minimum missiles must be fired so that the probability of the completely destroying the target is not less than 0.95?