Reading 4: Common Probability Distributions

Which of the following best describes a discrete random variable?

For a continuous uniform distribution defined between a lower limit a and an upper limit b, what is the probability that the random variable X takes on a value greater than b?

In a binomial distribution with n trials and probability of success p, what is the expected number of successes?

Which of the following is a key property of the normal distribution?

A portfolio manager wants to determine the probability that a portfolio's return will fall below a minimum acceptable level. Which measure should be maximized to minimize this probability?

How is a z-value calculated for a random variable X from a normal population?

For a lognormal distribution, which of the following statements is true regarding the possible values of the random variable?

What is the 95 percent confidence interval for a standard normal random variable?

If an investor has a holding period return of 20 percent over one year, what is the continuously compounded annual rate of return?

The Student's t-distribution approaches the standard normal distribution as:

Which of the following parameters is necessary to completely describe a multivariate normal distribution for the returns of n assets?

A chi-square distribution is bounded from below by:

Monte Carlo simulation is best described as a technique that:

If the probability of success in a single trial is 0.40, what is the probability of exactly 2 successes in 5 independent trials (Binomial distribution)?

What is the probability that a continuous uniform random variable defined between 2 and 10 takes on a value of exactly 5?

An analyst estimates the mean return of a stock to be 10 percent with a standard deviation of 20 percent. If returns are normally distributed, the 90 percent confidence interval for the return is:

Which of the following is a property of the standard normal distribution?

Shortfall risk is best defined as:

If an asset's price today is 100 and it increases to 110 over one year, what is the continuously compounded annual return?

Compared to the normal distribution, the Student's t-distribution has:

The F-distribution is defined by:

If a cumulative distribution function F(x) represents the probability that X is less than or equal to x, how is the probability that X lies between a and b calculated?

Which distribution is typically used to test the equality of variances of two normal populations?

A stock has an expected return of 12 percent and a standard deviation of 15 percent. If the threshold return is 2 percent, what is the Safety-First Ratio?

In a continuous uniform distribution ranging from 0 to 20, what is the probability that the random variable falls between 5 and 15?

What is the variance of a binomial random variable with n=10 trials and probability of success p=0.5?

When using Roy's Safety-First Criterion to choose among portfolios, which portfolio is preferred?

Which of the following is a characteristic of the lognormal distribution?

For a standard normal distribution, what is the probability that a value lies to the left of 0?

If the continuously compounded annual rate of return is 10 percent, what is the holding period return after 2 years?

What is a limitation of Monte Carlo simulation?

Which distribution describes the sum of squared values of n independent standard normal random variables?

In a binomial experiment with 1 trial, the distribution is called a:

For a normal distribution with mean 50 and standard deviation 5, what is the z-score of an observation of 60?

If a cumulative distribution function F(x) = 0.60, what does this indicate?

With 10 degrees of freedom, the t-distribution is:

Which of the following is true regarding a linear combination of normally distributed random variables?

If a stock's price is modeled using a lognormal distribution, what can be said about the stock's returns?

For a discrete uniform distribution with n possible outcomes, what is the probability of each outcome?

Roy's Safety-First Criterion states that the optimal portfolio maximizes:

What is the approximate probability that a normally distributed random variable falls within one standard deviation of the mean?

When constructing confidence intervals for small samples from populations with unknown variance, which distribution is most appropriate?

Which of the following is true about the F-distribution?

If a cumulative distribution function F(x) = x/10 for x in {1, 2, 3, 4}, what is F(3)?

What is the critical z-value for a 95 percent confidence interval?

In a simulation of stock option values, the process of generating random values for risk factors based on assumed distributions is a key step in:

If two events are independent, the probability of both occurring is determined by:

Which distribution uses the parameter 'degrees of freedom' equal to n - 1?

What is the lower bound of a normal distribution?

A key difference between a univariate and a multivariate normal distribution is: