Question

the class is EGEN 350 pleas i need the answers of questions 4,5 and 6

(3pts) An insurance company offers its policyholders a number of different premium payment options. For a randomly selected policyholder, let X = number of months between successive payments. If the CDF is as follows, fill in the pmf in the table provided? 4. 0.30 1sx <3 0.45 4 x<6 0.60 6 Sx < 12 1x2 12 Fx)0.40 3sx <4 P(X x) (3pts) A certain type of component is packaged in lots of four. Let X represent the number of properly functioning components in a randomly chosen lot. The probability mass function of X is given below. Find the value of the constant c so that P(X x) is a valid probability mass function. 5. P(X-a)-scx x-1,2, 3, or 4 0 otherwise Suppose that the probability that a grader will make a marking error on any particular question of a multiple-choice exam is 0.1. There are 10 questions and the questions are marked independently. a. (3pts) What is the probability that exactly one error is made? 6. b. (3pts) What is the probability that at least one error is made?

Answer 1

4)

x	1	3	4	6	12
P(x)	0.3	0.1	0.05	0.15	0.4

5)

for this to be valid: $\sum$xP(x)=c*(1+2+3+4)=1

c=1/10=0.1

6)

a)

P(exactly one error)=¹⁰C₁ (0.1)¹(0.9)⁹ =0.3874

b)P(at least one error)=1-P(no error)=1-(0.9)¹⁰ =0.6513