Let X be a random variable with probability density function f (x) = } 0, otherwise a. What is the value of c? b. What is the cumulative distribution function of X?
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- The marginal probability of good weather, G, is 0.6. The marginal probability of a highway accident, A. is 0.014. The joint probability of a highway accident and good weather is 0.006. Find the probability of a highway accident if you know the weather is not good. O a. approx. 0.02 O b. approx. 0.594 O c. approx. one O d. cannot be determinedThe wait time at a popular fast food restaurant is uniformly distributed between 2 and 10 minutes on average (a) Find the probability that you wait less than 4 minutes. (b) Find the probability that you wait between 8 and 10 minutes. (c) Explain why the answers to (a) and (b) are the same. Hint: draw the probability density function for a Uniform random variable. Explain with a graph and also without a graph.Suppose the probability density function for a uniform distribution ranging from 0 to 1. Thus the probability that the random variable X is between 0.20 to 0.70 is
- Suppose the probability density function for a uniform distribution ranging from 0 to 1. Thus the probability that the random variable Xis between 0.20 to 0.70 is O a. 1.00 O b. 0.20 Oc 0.50 O d. 0.70 GE NEXT PAGE to search 近Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal with a mean u= 7500 and a = 1750. A test result of x < 3500 is an indication of leucopenia. This indicates bone marrow depression that may result in a viral infection. a. What is the probability that on a single test x is less than 3500? b. A patient is given 3 tests at regular intervals. What is the probability that the average of the three tests is less than 3500?If X is normally distributed with mean 0 and variance 1, what is the probability density function of X2 ?
- please answer??Suppose the probability density function for a uniform distribution ranging from 0 to 1. The mean of the random variable X for this distribution is O a. 0.50 O b. 0.75 Ос. 0.25 d. 1.00Choose ALL THE CORRECT STATEMENTS in the following ones about probability distribution. i. Probability mass function indicates the probability distribution of a continuous random variable. ii. Probability mass function indicates the probability distribution of a discrete random variable. iii. The probability mass function of a discrete random variable X at a is denoted by P(X < a). iv. The probability function of a continuous random variable Y can be described by using P(Y= a).
- A motorcycle drives from Moraytato Lacson and back using the same course everyday. There are four stoplights on the course. Let x denote the number of red lights the motorcycle encounters going from Morayta to Lacson and y denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (x, y) is given by x y 0 1 2 3 4 0 0.01 0.01 0.03 0.07 0.01 1 0.03 0.05 0.08 0.03 0.02 2 0.03 0.11 0.15 0.01 0.01 3 0.02 0.07 0.1 0.03 0.01 4 0.01 0.06 0.03 0.01 0.01 (g) Give the standard deviation of X. Answer=A fair coin is flipped three times. Let X represent the number of heads to occur on the first two flips and Y the number of heads to occur on the last two flips. (a) Find the joint probability function, along with each marginal function, for X and Y. (b) Find cov(X, Y). (c) Are X and Y independent? Explain your answer. Hint: There are 8 outcomes for this expermient, e.g., if the outcome is HTT, then we have X = 1 and Y = 0.Suppose the weight of pieces of passenger luggage for domestic airline flights follows a normal distribution with u = 24 pounds and o = 6.3 pounds. (a) Calculate the probability that a piece of luggage weighs less than 28.8 pounds. (Assume that the minimum weight for a piece of luggage is 0 pounds.) (b) Calculate the weight where the probability density function for the weight of passenger luggage is increasing most rapidly. Ib (c) Use the Empirical Rule to estimate the percentage of bags that weigh more than 11.4 pounds. % (d) Use the Empirical Rule to estimate the percentage of bags that weigh between 17.7 and 36.6. % (e) According to the Empirical Rule, about 84% of bags weigh less than pounds.