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The success rate of corneal transplant surgery is 85%. The surgery is performed on six patients. (Adapted from St. Luke's Cataract & Laser Institute) (a) Construct a binomial distribution. (b)…
The number of planes arriving per day at a small private airport is a random variable having a Poisson distribution with $\lambda = 28.8$. What is the probability that the…
a. Items are packed into boxes of 1000, and each item has a probability of 0.001 of having some type of fault. What is the probability that a box will…
The number of parking tickets issued in a certain city on any given weekday has a Poisson distribution with parameter $\lambda = 50$. What is the approximate probability that a.…
Imagine you are in a game show. There are 4 prizes hidden on a game board with 10 spaces. One prize is worth \$100, another is worth \$50, and two…
A certain type of light bulb has lifetimes that follows an exponential distribution with mean 1000 hours. Find the median lifetime, i.e. the lifetime x such that 50% of the…
The probability that you will win a game is 0.45. (a) If you play the game 80 times, what is the most likely number of wins? (b) What are the…
It is often assumed that the auto traffic that arrives at the intersection during a unit time period has a Poisson distribution with expected value $m$. Assume that the number…
Let $T$ be the survival time and $T$ follows an exponential distribution. Derive the expression for survival function of $T$. Also obtain expression for force of mortality. Solution Let $T$…
Derive the expression for survival function of $T$, where $T$ is the survival time having Two parameter weibull distribution. Solution Let the survival time $T$ follows two parameter Weibull distribution.…
