let X be a random variable and X-B(9,0.49) find the mean (expected value) of the random variable X
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- В2. (a) Given the probability Venn diagram below for the two Events A and B find the probabilities: 0.6 0.5 A 0.2 (i) (ii) (iii) Pr( A 'OR' B) Pr( Not-A 'AND' Not-B) Pr( Not-A "OR' Not-B) (b) A random sample from a population of X with unknown mean but a known variance, o = 400, gives the following data: sample size, n= 125, Ex= 1750. (i) Give a point estimate of the population mean, u. (ii) Is this estimate biased or not. Give a reason. (ii) Derive a 95% confidence interval for the population mean, µ.Let a be a random variable representing the percentage of protein content for early bloom alfalfa hay. The average percentage protein content of such early bloom alfalfa should be u = 17.2%. A farmer's co-op is thinking of buying a large amount of baled hay but suspects that the hay is from a later summer cutting with lower protein content. A small amount of hay was removed from each bale of a random sample of 50 bales. The average protein content from the samples was determined by a local agricultural college to be -15.8% with a sample standard deviation of S = 5.3%- At a = .05, does this hay have lower average protein content than the early bloom alfalfa?What is E(T) where is a T random variable with 17 degrees of freedom?
- The probability distribution of the binomial random variable X is 3-x b(x; n, p) = (³) (¹) * (-²) ³**. x = 0,1,2,3. The standard deviation of X may be expressed as a simplest fraction equal to Find (a + b)².The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.3 minutes and a standard deviation of 2.5minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. (a) What is the probability that for 36 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)(b) What is the probability that for 36 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)(c) What is the probability that for 36 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)2 (a) Let Y be the random variable that counts the number of sixes which occur when a die is tossed 10 times. What type of random variable is Y? What is P (Y = 3), expected number of sixes,Var(Y )? (b) Let U be the random variable that counts the number of accidents that occur at an intersection in one week. What type of random variable is U? Suppose that, on average, 2 accidents occur per week. Find P(U = 2), E(U), and V ar(U). (c) Let X be the recorded body temperature of a healthy adult in degrees Fahrenheit. What type of rv is X? Estimate its mean and standard deviation, based on your knowledge of body temperatures.
- Let A be a random variable corresponding to the sum of the outcomes of two independent rolls of a fair 6-sided die (numbered from 1 to 6). Determine the variance of A.Q3: Find the expectation and the variance of X, where X is binomial random variable X ~ Binomial (n, p), Var(X)?Let X be a chi-squared random variable with 12 degrees of freedom. What is the probability that X is greater than 23? What are the steps to come to this conclusion?
- The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.6 minutes and a standard deviation of 2.8 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. USE SALT (a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.) 0.5432 (b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.) (c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)3 The median value y of a continuous random variable is that value such that F(y) = 0.5. Find the median value of the random variable in 90.5 = f(y) = 2 25 -Y, 0 ≤ y ≤ 5, elsewhere. 0,
