1. Read the webpage, https://en.wikipedia.org/wiki/Binomial_distribution , down to thesection, Mode and Median. Readthoroughly the example about the biased coin that comes up heads withprobability of 0.3. This variable can bedescribed as, X~Bi(n=6, p=0.3). Use thisexample to answer the following questions.

a. What is the expected value of this variable?

b. What is the expected number of heads if this coin is tossed6 times? Same answer as in part 2.a. butin different words.

c. What is the probability that the number of heads out of 6tosses of this unfair coin is less than 2?

d. What is the probability that the number of heads out of 6tosses of this unfair coin is more than 2?

e. What is the probability that the number of heads out of 6tosses of this unfair coin is at least 2?

f. What is the probability that the number of heads out of 6tosses of this unfair coin is at most 2?

2. Assume that 25% of all accounting audits identify anaccounting error and that 8 audits were completed. The variable of interest is the number ofaudits that identify an accounting error out of the 8 audits. The distribution of this variable isdescribed as X~Bi(n=8, p=0.25). Use thisinformation to answer the questions below. Use this online calculator, if you want: http://stattrek.com/online-calculator/binomial.aspx

a. What is the expected number of audits that will identifyaccounting errors?

b. What is the probability of 2 or more accounting errors beingidentified in the 8 audits?

c. What is the probability of 3 or more accounting errors beingidentified in the 8 audits?

d. What is the probability of 4 or more accounting errors beingidentified in the 8 audits?

e. What is the probability of 5 or more accounting errors beingidentified in the 8 audits?

f. What is the probability of 6 or more accounting errors beingidentified in the 8 audits?

g. What is the probability of 7 or more accounting errors beingidentified in the 8 audits?

h. What is the probability of 8 or more accounting errors beingidentified in the 8 audits?