18.X.3. Properties of Binomial Distribution

Try these first

1. 1.

   What is the mean of a binomial distribution with n = 6 and p = 0.4?

   Hint

   Use the formula E(X) = np.

2. 2.

   Calculate the standard deviation for a binomial distribution with n = 8 and p = 0.5.

   Hint

   Recall the standard deviation formula σ = √(np(1 - p)).

3. 3.

   What is the formula for the mean of a binomial distribution?

   • np
   • n(1-p)
   • p/n

   Hint

   Think about what the mean represents in your trials.

4. 4.

   True or False: The variance of a binomial distribution is calculated as np(1-p).

   • True
   • False

   Hint

   Recall the definition of variance and its role.

5. 5.

   A professor conducts an experiment allowing students to respond with either a 'yes' (success) or 'no' (failure). If the probability of a 'yes' is 0.4 and there are 12 trials, calculate the skewness and kurtosis.

   Hint

   Use the formulas provided for skewness and kurtosis.

6. 6.

   A game involves rolling a die 8 times. Determine the variance and standard deviation of rolling a 3, with the probability of rolling a 3 denoted as 1/6.

   Hint

   Count on the binomial formula for variance and take the square root for SD.