A system consisting of one original unit plus a spare can function for a random amount of time X. If the density of X is given (in units of months) by the following function. What is the probability that the system functions for at least 5 months?

[ f(x) = left{ begin {array} ( Cx e^{-x/2} & x gt 0 \ 0 & xleq 0 end {array} right. ] The question aims to find the probability of a function for 5 months whose density is given in units of months. The question depends on the concept of Probability Density Function (PDF). The PDF […]

In how many different orders can five runners finish a race if no ties are allowed?

The purpose of this question is to understand the concepts of permutations and combinations for evaluating a different number of possibilities of a given event. The key concepts used in this question include Factorial, Permutation and Combination. A factorial is a mathematical function represented by the symbol ! that operates only on the positive integers. In fact, […]

Suppose S and T are mutually exclusive events P(S)=20.

This question aims to find the P (S) or P (T) of two mutually exclusive events S and T if the probability of P (S) is given. Two events are called mutually exclusive if they do not occur at the same time or simultaneously. For Example, when we toss a coin, there are two possibilities […]