Question

1. Assuming a normal distribution with a mean of 5 and standard deviation of 1.2, what is the P(X = 6)?
   1. 0
   2. 0.2033
   3. -0.8333
   4. 0.8333
      
      
2.   Assuming the expected value of a distribution is 4 and the standard deviation is 0.85, what would be the expected value if a constant of 1 added to each value of x?
   1. 4.00
   2. 4.85
   3. 5.00
   4. 5.85
      
      
3. What distribution would you use if you want to find the expected number of heads when you flip a coin 100 times?
   1. Normal
   2. Uniform
   3. Geometric
   4. Binomial
      
      
4.   What distribution would you use if you want to find the expected number of times you have to roll a die until you get a 6?
   1. Normal
   2. Uniform
   3. Geometric
   4. Binomial
      
5.   What is the expected number of times you will get heads if you flip a fair coin (50/50 chance of heads or tails), if you flip the coin 5,000 times?
   1. 0
   2. 50
   3. 2500
   4. 5000

Answer 1

Solution:

Assuming a normal distribution with a mean of 5 and a standard deviation of 1.2, what is the P(X = 6)?

Answer: 1. 0

Because the probability of a continuous random variable at a single point is always 0

  Assuming the expected value of a distribution is 4 and the standard deviation is 0.85, what would be the expected value if a constant of 1 added to each value of x?

Answer: 5

Using the property of expected value , we have:

What distribution would you use if you want to find the expected number of heads when you flip a coin 100 times?

Answer: Normal

Here binomial distribution would approach to a normal distribution as the number of trials got increased and probability is 0.5

What distribution would you use if you want to find the expected number of times you have to roll a die until you get a 6?

Answer: Geometric

The geometric distribution is used when we are interested in knowing the first success after several failures

  What is the expected number of times you will get heads if you flip a fair coin (50/50 chance of heads or tails), if you flip the coin 5,000 times?

Answer: 2500

Since the probability of getting a head is 0.5. Now if the coin is flipped 5000 times, then the expected number of heads are: