1. A shipment of 7 computers contains 2 defective units. A forestry company makes a random purchase of 3 of the units. If X is the number of defective units purchased by the company, find the probability distribution of X. Express the results graphically as a probability bar graph. 2. A potential customer for a $90,000 fire insurance policy possesses a home in an area which, according to experience, may sustain a total loss in a given year with probability of 0.001and a 50% loss with probability 0.01. Ignoring all other partial losses, what premium should the insurance company charge for a yearly policy to make 10% above the break-even point? 3. From a group consisting of 2 Douglas-fir, 3 hemlock and 1 balsam seedlings, 3 are to be randomly selected. Let X denote the number of hemlocks, and Y the number of Douglas-firs. a. Find the joint probability distribution of X and Y. b. Find the marginal probabilities of X and Y. c. Are X and Y independent? d. Find the covariance of X and Y. e. Solve for E(X + Y). f. Solve for E(X – Y). g. Solve for E(XY). 4. An oil well drilling company generally drills four wells per month. The probability distribution of successful attempts out of the four wells is given by No. of successes (x) 0 1 2 3 4 Probability of successes f(x) 0.1 0.4 0.3 0.1 0.1 Find the expected number of successful wells and the standard deviation. Construct the interval µ ± 2σ and give an interpretation using Chebyshevs theorem. Discrete and Continuous Distributions 1. An expert shot bits the target 95% of the time. What are the probabilities that he will miss the target: a. for the first time on the fifteenth shot? b. at least one time during fifteen shots? c. for the second time on the eighteenth shot? 6/8/2015 Assignment Instructions – 2015SA-FRST231-... data:text/html;charset=utf-8,%3Cb%20style%3D%22margin%3A%200px%3B%20padding%3A%200px%3B%20color%3A%20rgb(51%2C%2051%2C%2051)%3B… 2/2 2. The number of weekly breakdowns of a given machine in a sawmill is a random variable having a Poisson distribution with µx = 0.4 . What is the probability that the machine will break down at least once during the coming week? 3. According to the theory of genetics a certain cross of guinea pigs will result in red, black and white off-springs in the ratio of 8:4:4. Find the probability that among 6 such off-springs 4 will be red, 1 black and 1 white. 4. A forester plants 5 seedlings selected at random from a bag containing 5 Douglas-fir and 6 hemlock seedlings. What is the probability that 2 firs and 3 hemlocks were planted? 5. The trees in a cutting block have an average diameter of 35 cm, have a standard deviation of 6 cm and are normally distributed. For appraisal purposes we need to know: a. What proportion of trees is less than 25 cm in diameter (for pulp mill use)? b. What proportion of trees is greater than or equal to 25 cm and less than or equal to 40 cm (for sawmill use)? c. What proportion of trees is greater than 40 cm (for plywood use)? Assume that the trees can be measured to the nearest 0.1 cm. 6. You are the manufacturer of chain saws and are prepared to replace free all saws that fail while under guarantee. If you are willing to replace only 3% of the saws that fail, how long a guarantee should you offer? Assume that you know that the lives of the saws follow a normal distribution with an average of 12 years and a standard deviation of 2 years