queution is worth to points Wite your answes on the blan p Nso oal ulators are a

Question

queution is worth to points Wite your answes on the blan p Nso oal ulators are allowet Once you got your anawer to something pl sagosd into a caleulator to get the final anewe, do NOT slboplity fusth Fill im the blanks For hull points, e as specific as posuible (a) Let s be the sample space of one experiment, ond let e on ovens of sample space iii) P(A")-1 (b) It A and B are independent events, then P(ALD) (e) If A and B are mutually exclusive evente, then PEAL (d) If X is a random. vvrialle and EtX)-2, then E[3X ' iol- (e) If N is a random variable and Vartx)- b, then Var(ax3) (t) Let X be a continuous random variable with a probability density funeion (pdt) of f(a) i)(a)for all e (-oo, oo) (s) Let X and Y be continuous random variables with a joint probability density function (pdt) of f(a,p). PXDy>2) 2 (a) How many ways are there to arrange the letters P O RTMORRIS (b) An ura contains 6 white bals, 4 black balls, and 5 red balls. You pick thres balls (without replacement) from the urn. What is the probability that you chose 2 white balls and 1 black ball? The order you choose the balls in is not important 3, 80% of dogs in New York wear coats in the winter, and 30% of dogs in New York wear booties in the winter, 20% of dogs in New York wear both coats and booties in the winter. (a) What percentage of New York dogs wear only booties (and not conta) in the winter? (b) What percentage of Nev winter? 4, Your name is spelled correctly on 15% of the junk mail you receive, and incorrectly on the other 90%. Your name is spelled correctly on 95% of the legitimate, non- nk mail that you receive, and incorrectly on the other 5%. Approximate! y 60% of the mail you receive is junk mail. If you receive a piece of mail with your name spelled correctly, what is the probability that it is junk mail?

Explanation / Answer

a) i) 0 <= P[E] <= 1

because probability can not be negative , and it cannot exceed 1.

ii) P (S) = 1

probability of S includes everything. so it has a probability 1.

iii) P (Ec) = 1 - P (E)

b. If A and B are independent events then P(A|B) = P (A intersection B) / P(B) = P(A) P(B) / P(B) = P(A)

c. If A and B are mutually exclussive events then P(A|B) =  P (A intersection B) / P(B) = 0/P(B) = 0

d. E(X) = 2

E( 3 X + 10) = 3 E(X) +10 = 3*2 +10 = 16

e. V(X) = 5

V(2X+3) = 4 V(X) + 0 = 4 V(X) = 4*5 = 20

f. i) integration from -infinity to +infinity is always 1

2) there are total of 10 letters.

there are 2 O's and 3 R's

required number of ways = 10! / 2! 3! = 302400

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.