A sequence of random variables $$X_1,X_2,\ldots,X_n,\ldots$$​​ is said to converge in probability to a constant A if for any $$\epsilon>0$$​​, we have

A sequence of random variables $$X_1,X_2,\ldots,X_n,\ldots$$​​ is said to converge in probability to a constant A if for any $$\epsilon>0$$​​, we have

The function $$\phi(t)$$​ is a characteristic function of a random variable if

If $$P(A\cup B)=\frac{5}{6}, P(A\cap B)=\frac{1}{3}$$​, and $$P(\bar A)=\frac{1}{2}$$​ then P(A/B) is equal to

Die A has four red and two white faces whereas die B has two red and four white faces. A single coin is flipped once. If it falls head the game starts with the throwing of die A and if it falls tail die B is to be used first. The probability of getting a red face at any throw of any die is

If the events S and T have equal probabilities and are independent with P(S ∩ T) = p > 0, then P(S) is

Three numbers chosen from 1 to 20. Probability that they are not consecutive is:

The median and mode of a frequency distribution are 26 and 29 respectively. Then the mean is:

If the probability that an individual suffers a bad reaction from an injection of a given serum is 0.001, then using Poisson's distribution, the probability that out of 2000 individuals, exactly 3 will suffer a bad reaction is:

When a random variable can take on any values within a given range where the probability distribution is continuous, it is called:

An experiment succeeds twice as often as it fails. The probability that in the next six trials, there will be at least 4 successes, is: