2. Read the webpage, https:/len.wikipedia.org/wiki/Binomial distribution, down t

Question

2. Read the webpage, https:/len.wikipedia.org/wiki/Binomial distribution, down to the section, Mode and Median. Read thoroughly the example about the biased coin that comes up heads with probability of 0.3. This variable can be described as, X-B(n=6, p=0.3). Use this example 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 tossed 6 times? Same c. What is the probability that the number of heads out of 6 tosses of this unfair d. What is the probability that the number of heads out of 6 tosses of this unfair e. What is the probability that the number of heads out of 6 tosses of this unfair f. What is the probability that the number of heads out of 6 tosses of this unfair answer as in part 2.a. but in different words. coin is less than 2? coin is more than 2? coin is at least 2? coin is at most 2? I

Explanation / Answer

X ~ Bi(n=6, p = .3)

a. Expected value of this variable : np = 6*.3 = 1.8

b. Same as above,i.e. 1.8. To put it in words out of the 6 tosses , we expect 1.8 tosses to end up ion head with the given params of binomial distribution

c. P(X<2) = P(X=0)+P(X=1) = 6C0(.3^0)(.7^6)+6C1(.3^1)(.7^5) = 0.420175

d. P(X>2) = 1-P(X<=2) = 1- (6C0(.3^0)(.7^6)+6C1(.3^1)(.7^5) +6C2(.3^2)(.7^4) ) = 1-0.74431 = .2567

e. P(X>=2) = 1-P(X<=1) = 1-0.420175 = .5798

f. P(X<=2) = (6C0(.3^0)(.7^6)+6C1(.3^1)(.7^5) +6C2(.3^2)(.7^4) ) = .2567

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