Question

For each of the following, find the constant c so that p(x) satisfies the condition of being a probability density function of a random variable X:
I. p(x) = c(2/3)^x, x ∈ N
II. p(x) = cx, x ∈ {1,2,3,4,5,6}

Answer 1

Question #18775The probability that i have to wait at the traffic lights on my way to school is 0.25,find the probability that , on two consecutive mornings, i have to wait on at least one morning. .

Solution. Denote by $A_{1}=${have to wait in the first day}, $A_{2}=${have to wait in the second day}. Thus $P(A_{1})=P(A_{2})=0.25$ and $A_{1},A_{2}$ are independent. We are to find $P(A_{1}\cup A_{2})=P(A_{1})+P(A_{2})-P(A_{1}\cap A_{2})=2P(A_{1})-P(A_{1})^{2}=0.5-0.0625=0.4375.$

Answer. 0.4375.