Question : An infinite sequence of independent trails is to be performed . Each trail results in a success with the probability p and a failure 1-p . What is the probability that i) at least 1 success occurs in the first n trails ii) exactly k success occur in the first n trails iii) all trails resu...
Problem : If the probability of X is given by f(x) = \begin{cases} x/2, & 0 < x < 1 \\ 1/2, & 1 < x < 2 \\ (3-x)/2, & 2 < x < 3 \\ 0 & elsewhere \end{cases} find the expected value of g(x) = X^2 - 5X + 3 Solution : \int\limits_{0}^{1} . g(x) \frac{x}{2...
Question : The average working-set size X of a program is normally distributed with the unknown mean \mu and a known variance \sigma 2 =81 . The program was executed 36 times and the average working set size for each run recorded. The sample mean was computed to be 100 page frames . Assuming success...
Question: In answering a question on a multiple choice test , an examine either knows the answer or he guesses or he copies. Suppose each question has 4 choices. Let the probability that examine copies the answer is 1/6 and the probability that he guesses is 1/3. The probability that his answer is c...
Question : Suppose A and B are two events with P(A)=0.5 and P(A \cup B)=0.8 i) For what value of P(B) would A and B be mutually exclusive ii) For what value of P(B) would A and B be independent Solution i) if P(A) = 0.5 and P(A \cup B)=0.8 then P(B) = P(A \cup B) - P(A) = 0.8 - 0.5 = 0.3 (Is thi...
The rule of independent events P(A \cap B) = P(A) . P(B) , But how do i use this as i dont know the value of P(A \cap B) We also have P(A\cup B)=P(A)+P(B)-P(A\cap B) How should i use this in solving the 2nd question ii) For what value ...
Question : X is a random variable which takes 3 values -1,0,1 with equal probability i.e. P(x=-1) = P(X=0) = P(X=1) = 1\3 Find E(X) and Var(X) Solution : E(X) = 0 _{(is this correct?)}