# HW4 - S tat 4714 HW 4 Fall 2010 Due F riday 9/17 at 1:15pm...

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Stat 4714 HW 4 Fall 2010 – Due Friday 9/17 at 1:15pm NOTE: YOU WILL NOT GET THIS HW BACK BEFORE THE EXAM. YOU SHOULD MAKE A COPY OF IT BEFORE TURNING IN SO YOU CAN COMPARE YOUR WORK TO THE SOLUTIONS. (1) Both m’ x (t) and m’’ x (t) for the binomial distribution are given below. a. Find E(X 2 ). b. Find σ 2 . c. Find σ . (2) Identify the distribution for each using the mgf: a. m x (t) = b. m x (t) = (.2 +.8e t ) 7 c. m x (t) = (.4e t ) 13 /(1 - .6e t ) 13 (3) How many times would you expect to toss a balanced coin in order to obtain the first head? (4) A new surgical procedure is successful with a probability of .8. Assume the operation is performed 5 times and the results are independent of one another. What is the probability that all five operations are successful? (5) A certain type of tree has seedlings dispersed in a large area, with the mean density of seedlings being approximately five per square yard. If a forester randomly locates ten 1-yard sampling regions in the area, find the probability that none of the regions contain seedlings. (6) A geological study indicates that an exploratory oil well drilled in a particular region should strike oil

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HW4 - S tat 4714 HW 4 Fall 2010 Due F riday 9/17 at 1:15pm...

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