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prac1-solns

# prac1-solns - 1(20 points There are two urns The ﬁrst has...

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Unformatted text preview: 1. (20 points) There are two urns. The ﬁrst has 3 red balls and 5 blue balls, the second has 6 red balls and 100 blue balls. A coin is ﬂipped. If heads comes up a uniform random ball is picked from the ﬁrst urn, if tails comes up a uniform random ball is picked from the second. Given that the picked ball is blue, What is the conditional probability that the coin was a heads. H ievmi Coin Lamls B 1 event boll élqﬁ 2. (20 points) A hand of 4 cards is picked from a standard deck. Compute a. (7 pts) the probability that every card in the hand is of the same suit. (“i/(\$1 (Loose, Sn {1' i—:’ Ckmmc deﬁ (5%} b. (717233) The hand contains exactly one pair. W )16 0 “ C/aww, cu, Chaseuk/ .' ('?)(3\(E(‘f)(ﬁ‘i m""‘“°’&‘ (a) Y/(W/ MM H“ m M (if) (23‘ Wk 16‘“ c. (6 pts) Every card in the hand is a different suit and a different rank. CLuoS¢ (’9 Chum: rain ((3 I3 11' (£11014: £ HQ €40qu WALK (53(i)(\]( \) i Sal.) 0v 294%: (:2 «1 HQ (WNW/s) W» 64’me / 3. (20 points) X is a continuous random variable with pdf ﬁx) 2 Zea—2"” if a: Z 0, and f (:0) = 0 otherwise. Compute a. (719255) IP’(X 6 C1) where C1 = N = {1,2,3,4, . . }. FP()<‘\\°[P(X‘U ‘ O m QZC’ZXJAOO‘ M IPCXc-C) v EWWH vQ kw b-(7Pts) P<X23) 0.0 «1x -2199 4 f2?” JX 1'6, ‘2 € 3 3 0- (6 MS) MK 2 31X 2 2), 00 4x 4! POO/A" gas-“3A 3 ‘6 k l: e x '2 , [P999 :53; 16/2 “XX/5W1)“ W32) W ‘ 4. (20 points) TWO fair dice are rolled. a. (10 pts) Let X denote the absolute value of the difference between the rolls. Compute the pmf p(az) of X. b. (10 pts) Determine the probability that the product of the two rolls is greater than the sum of the two rolls. he: H {eqﬁz Oné Ea i r 900th 5 SW0 W“ ‘E 0 53 M m ”W (In 6) ((313 “17/4 aghast“ QC mlfs Is‘ (wear (2)2) 5. (20 points) a. (10 pts) Could F(m) = g for as = 0,1,2,3. .. denote the cdf of a random variable X. Why or Why not? FCJ I} VsQequsfm. , Cow/0L ”ML 63 CD]: (W [OJ- (9mg) MFMUQMﬁ) b. (10 pts) A continuous random variable X has pdf f (3L) 2 515 for a: Z 1, 0 otherwise. Compute the cdf and pdf of Y : X 2. We 5th t: (j-mﬁ ' 1 ' W " ‘ z A... 7 ...
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prac1-solns - 1(20 points There are two urns The ﬁrst has...

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