41. Show by using convolution that distribution of a sum of independently and identically distributėd variables S, = X1 + X2+... + Xn
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- Assume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. Construct a sample space for the torture test. Use S for survive and F for fail.Find the probability of each event. Getting 2 red eggs in a single scoop from a bucket containing 5 red eggs and 7 yellow eggsApproximately 8% of students at a local high school participate in after-schoold sports every year of hs. A group of 60 seniors is randomly choosen. Of interest is the number who participated in after school aports every year of hs. In words define the variable X, list the values that x may take on, Write the distribution of X mathmatically with correct notation, how many seniors in this group are expected to have participated in after school sports every year of hs, Find the probability that no seniors participated in after school sports every year of hs- list the Excel command used, Based on numerical values would you be suprised if none of the seniors participated in after school sports every year of hs and why?
- A box contains 5 Balls labeled with the number "1", 3 balls labeled with the number "2", and 1 ball labeled with the number "3". Two balls are selected, without replacement. Let X be the total of the values on the two balls. Find the mean of X.Let X have a uniform distribution on the interval (4, 10). Find the probability that the sum of 2 independent observations of X is greater than 19.Let X have a uniform distribution on the interval (7, 12). Find the probability that the sum of 2 independent observations of X is greater than 23.(26) Let X b(8,- Var-x) and distribution function.
- Let X₁ Bin(n1, p) and X₂ ~ Bin (n2, p). Find the distribution function of Y = X₁ + X₂. Assume X₁ L X₂. ~For a highway, the car's speed has a uniform distribution [50,90]. Cars are stopped if speed X is greater than 70(mph). The price of a speeding ticket is equal to Y = 15 + (1/10)X(X-70). What is the probability that a stopped car is/was going faster than 85 mph? For each car stopped, the Var(X) is equal to what?If 25% of the oranges produced by a farm is defective in a random sample of 20 oranges, then if the variable X represents the number of defective oranges in the required sample: Calculate (X> 3) exactly
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