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Exam 5: Continuous Random Variables and Probability Distributions

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Question 91

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One must use caution concerning finance models in that continuous clear observation and thinking cannot be replaced by models developed from:

A) foreign markets.
B) futures.
C) past events.
D) human error.

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Question 92

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose that the time between successive occurrences of an event follows an exponential distribution with mean 1/λ minutes.Assume that an event occurs. -Show that the probability that more than 4 minutes elapses before the occurrence of the next event is e^-4λ.

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P(X > 4)= ...

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Question 93

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Let the random variable Z follow a standard normal distribution.Find the value k,such that P(Z > k) = 0.39.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The number of orders that come into a mail-order sales office each month is normally distributed with a mean of 298 and a standard deviation of 15.4. -What is the probability that in a particular month the office receives more than 310 orders?

Because the probability of any specific value is 0 for a continuous random variable,the expected values for continuous random variables are computed using:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let the random variable Z follow a standard normal distribution. -Find the value k such that P(-0.71 < Z < k)≈ 0.67

The combinations of continuous random variables whose development is based on operation with expected values and does not depend on the particular probability distribution are called:

A function of continuous random variables which allows for graphical interpretations of their probability structure is called the:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Consider a random sample of size n =1800 from a binomial probability distribution with P = 0.40,and X = number of successes. -Find the probability that the percentage of successes is greater than 0.42

The shape of the normal probability density function is a symmetric bell-shaped curve centered on the:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The number of orders that come into a mail-order sales office each month is normally distributed with a mean of 298 and a standard deviation of 15.4. -What is the area under the normal curve between Z = -2 and Z = 0?

The normal probability distribution provides a very close approximation to the binomial probability distribution if np(1 - p)> 5,where n is the number of trials and p is the probability of success in any trial.

Let the random variable Z follow a standard normal distribution.Find the value k,such that P(-k < Z < k) = 0.78.

Let X₁,X₂,...... ,X_k be a set of k continuous random variables.The function F(x₁,x₂,..... ,x_k) which defines the probability that simultaneously X₁ < x₁,X₂ < x₂ and so on is called a:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let the random variable Z follow a standard normal distribution. -Find the value k such that P(Z > k)= 0.83

Linear functions of random variables have many applications such as in the case of car dealership sales.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Consider a random sample of size n =1800 from a binomial probability distribution with P = 0.40,and X = number of successes. -Find the probability that the percentage of successes is between 0.38 and 0.43

The owner of a fish market determined that the average weight for a catfish is 3.4 pounds with a standard deviation of 0.8 of a pound.A citation catfish should be one of the top 2% in weight.Assuming the weights of catfish are normally distributed,at what weight (in pounds) should the citation designation be established?

The continuous random variable X is uniformly distributed over the interval [a,b].The mean of the probability distribution of X is:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A continuous random variable X has the probability density function: f(x)= 2e^-2x,x ≥ 0. -Find the mean and standard deviation of X.