Common Probablity Distributions

12 questions

1. 1. Which of the following is the most accurate way to standardize any normal variable (X)?
   Subtract the mean of X from X and then divide it by the standard deviation of X.Divide the mean of X by the standard deviation of X.The mean of X is the standardized normal variable.
2. 2. Which of the following is true about the sum X + Y of two independent normal random variables X and Y?
   It is normal only if X and Y have the same mean.It is always normal.It is chi-squared.
3. 3. Suppose you purchased a lottery ticket and you can either win $10,000 with a probability of 0.10 or win nothing. Suppose X represents the amount you win. X will have a:
   Normal distributionUniform distributionBernoulli distribution
4. 4. You have a pool of stocks having either value or growth stocks. The probability of selecting a value stock is 0.60. You are going to pick up 5 stocks. Assuming binomial distribution, what is the probability of picking 2 value stocks?
   0.230.400.42
5. 5. Suppose you do day trading every day for next n days. Each day, the probability of you making a profit is p. Suppose X denotes the number of days you win, the expected number of hits is:
   np(1-p)npn(1-p)
6. 6. Suppose you do day trading every day for next 5 days. Each day, the probability of you making a profit is 0.75. Suppose X denotes the number of days you win. The variance of X is:
   3.750.93751.25
7. 7. A standard normal distribution has:
   The mean equal to the varianceMean equal 1 and variance equal 1Mean equal 0 and variance equal 1
8. 8. Which of the following is NOT an example of a continuous random variable?
   The time required to run a mile.The outcome of a roll of a die.The amount of rainfall in a town.
9. 9. An investor wants to earn minimum 5% returns over the next year. He has to make a choice between the following three portfolios.

   

   According to Roy's Safety-First criterion, which portfolio should he prefer?

   Portfolio APortfolio BPortfolio C
10. 10. Which of the following statements about lognormal distribution is least accurate?
    It is always positive with positive skew.If variable X is lognormal, then Ln(X) is normalThe sum of lognormal variables is lognormal.
11. 11. With continuously compounded rate of return r, the future stock price is expressed as follows: St = S0*EXP(r). If r is normally distributed, what can be said about the stock price (St)?
    It will be normally distributedIt will be lognormally distributedStock prices have binomial distribution
12. 12. Which of the following is a major drawback of using Monte Carlo simulation method to price assets or calculate VaR?
    Inability to handle assets with non-linear exposuresMakes assumption of normal distributionTakes a lot of computational power