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- Suppose X is a random variable defined as final cost of project estimated cost of project which has a PDF as follows: [0 xa a. Determine the value of a. b. What is the probability that the final cost of a project will exceed its estimated cost by 25%? c. Determine the mean value and standard deviation of X..mp4 nected 5: Hi 2) Suppose that X is a random variable having a probability density function là a Show whether or not bba9b078-e2f7-4....mp4 f(x; B) = Canceled 2 2 1 Χ. B 98% Confidence interval for ß if a random sample is given by 2.4, 4.6, 3.3, 3.1, 4.6, 2.2, 3.8 xe 0, elsewhere x > 0 is a pivotal quantity, Explain and if yes construct a 107249143202886, mp4 ✿ 4753e7db-6118-mp 14°C GES INCLUDING COVER PAGE.The probability that the standard normally distributed variable is between 1.011 and 2.8 is approximately equal to.
- Is the following random variable discrete or continuous? Let X represent the number of books in a random professor's office.Let theta be the unknown market share that a company has for its primary product. Uncertainty in theta is represented by a probability density function of the beta distributional form with a = 54 and b = 46. You have developed the posterior distribution for theta after observing that 64 out of a random sample of 90 customers used the product. Which statement is correct? O A. In the sample, the proportion of people who used the product is greater than the expected proportion based on the prior, but this discrepancy has not affected the mean of the posterior distribution. B. In the sample, the proportion of people who used the product is less than the expected proportion based on the prior, and has led to the posterior distribution having a mean smaller than the prior mean but greater then the sample mean. O C. In the sample, the proportion of people who used the product is greater than the expected proportion based on the prior, and has led to the posterior distribution having a mean…Find the mean and variance of X given the following probability density function:
- Find the following probabilities for the standard normal random variable ?.1. The loss due to a fire in a commercial building is modelled by a random variable X with density function Let X be a random variable with probability distribution table given below 10 20 50 100 P(X=x) | 0.4 | 0.3 | 0.15 | 0.1 | 0.05 Prepare the cdf of X.QUESTION 4 The probability density function for the time taken to complete a 1-hour test (X) by students is given by a) b) c) Find the value of c. f(x) = {cx² + x ! ) 0≤x≤1 elsewhere Find the probability that a randomly selected student will finish in at least half an hour. Calculate the variance of X.
- Why is the probability that a continuous random variable equals a specific number zero? That is, why is P(X=b)=0 for any number b?Let Z be the standard normal random variable. Find the value of z for which Pr[Z<z]=0.9943.A fair coin is flipped until the first tail appears. The player wins $2 if it occurs on the first flip, $4 if on the second flip, $8 if on the third flip and, in general, $2k if it occurs on the kth toss. Let X be a random variable that denotes the player's winnings. What is the pdf of X? Show that it satisfies the conditions required to be a proper pdf. What is the value of expected winnings? If the price to play this game was $10,000, would you play? Explain your answer.
