In a Poisson distribution 3 P(X = 2) = P(X = 4), then find the parameter of the distribution.

If the mean of the binomial distribution with 9 trial is 6, then find the variance.

If the mean of the binomial distribution is 20 and standard deviation is 4, then find the number of events.

Suppose X is a binomial variate X ~ B (5, p) and P(X = 2) = P(X = 3), then find p.

If 10 coins are tossed, find the probability that exactly 5 heads appears.

Students of a class were given an aptitude test. Marks were found to be normally distributed with mean 60 and S.D. 5. Find the percentage of students who scored more than 60 marks.

In a packet of 50 pens, 10 are defective, 10 pens are selected at random. What is the probability that atleast one is defective.

The random variable X has the normal distribution f(x) = \(C{ e }^{ -\left( \frac { x-100 }{ 50 } \right) ^{ 2 } }\), then find the value of C.

If you buy a lottery ticket in 50 lotteries, in each which your chance of winning a prize is \(\frac { 1 }{ 100 } \). What is the approximate probability that you will win a prize at least once (e-0.5 = 0.6066). 

The probability of the happening of an event X is 0.002 in an experiment. If an experiment is reported 1000 times, find the probability that the event X happens exactly twice? (e^-2 = 0.1353)

In a hurdles race, a player has to cross 10 hurdles. The probability that he will clear each hurdle \(\frac{5}{6}\) is what is the probability that he will knock down fewer than 2 hurdles?

Five dice are thrown simultaneously. If thee Occurrence of an even number in a single die is considered a success, find the probability of atmost 3 successes.

An unbiased die is thrown again and again until three sixes are obtained. Find the probability of obtaining 3^rd six in the sixth throw of the die. 

A die is thrown 20 times. Getting a number greater than 4 is considered as success. Find the mean and variance of the number of success.

A die is tossed thrice. Getting an even number is considered as success what is the variance of a binomial distribution?