Test: Distribution Of Random Variables - Commerce MCQ

We have ,
P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4

If S is the sample space associated with a random experiment. Then a real valued function which assign to each element of S, a unique real number is called a random variable.

A random variable is a numerical description of the outcome of a statistical experiment. It can be any outcome from some chance process, like how many heads will occur in a series of 20 flips etc. So as it is related to the chance of an event. Therefore its domain is the sample space of random experiment and as chance of occuring can never be a fraction or a negative number. So range is the set of real numbers.

The number of ways in which two balls can be represented are {(RR), (RB), (BR), (BB)}
Let X represent the number of black balls. Possible values of X are:
 X (RR) = 0, X (RB) = 1, 
 X(BR) 1 and X (BB) = 2.
Therefore the possible values of X are 0, 1 and 2.

As we known that a random variable which can assume all possible values within a given interval is called a continuous random variable.

P(5) = 0.01, P(6) = 0.02, P(7) = 0.17
P(X ≥ 5) = P(5) + P(6) + P(7)
= 0.01 + 0.02 + 0.17
= 0.20

The sum of all the probabilities of all the events of an experiment is 1. If a random variable X assume values x₁, x₂, x₃, …, x_n with the corresponding probabilities p₁, p₂, p₃, …, p_n. Then P₁ + P₂ + P₃ +…..+ P_n = 1