# Discussion Problem_ (1) Classic List Threaded 7 messages Open this post in threaded view
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## Discussion Problem_ (1)

 Q1) Let X be a random variable with density function f(x) such that P(X≥0)= 1.Then for a given number t > 0 which of the following is true (i) P(X≤t) ≤ E(X)/t (ii) P(X≥t) ≥ E(X)/t (iii) P(X≥t) ≤ E(X)/t (iv) None of the above Q2) 1. Consider two random variables X and Y, each taking values in {1, 2, 3}. Let their joint PMF be such that for any 1 ≤ x, y ≤ 3, Pr (X = x, Y = y) = f(x, y) = 0,  if (x, y) ∈ {(1, 3), (2, 1), (3, 2)} Pr (X = x, Y = y) = f(x, y) > 0,  otherwise Then, (i) X and Y can be independent or dependent depending upon the strictly positive values. (ii) X and Y are always independent. (iii) X and Y can never be independent. Q3) The letters of the word "MOTHER" are permuted, and all the permutations so formed are arranged in alphabetical order as in a dictionary. Then the number of permutations which come before the word "MOTHER" is (i) 503 (ii) (6!/2) - 1 (iii) 308 :)
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## Re: Discussion Problem_ (1)

 This post was updated on .  no. of words with E - 5! - 120                    with H - 5! - 120                    with ME- 4!   24                    with MO - 4!   24                    with MOE- 3!     6                     with MOH -3!    6                     with MOR -3!    6                     with MOTH- 2!   2 = 308 = ANS                                             with MOTHER = 309
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## Re: Discussion Problem_ (1)

 i am getting option 3 for all the the three questons. please tell me if i am wrong.
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## Re: Discussion Problem_ (1)

 hello duck:) i did the second question by taking examples and i could easily eliminate the options and get iii as the ans, and the third was straight fwd. in the first however, i did it by putting values . it was a very lengthy way and i am not sure wthr i am write or not. please along with the answer key if u could tell how to approach the first ques in a more formal manner. thankyou
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## Re: Discussion Problem_ (1)

 Hi.. :) Well done. Q1) Hint: Just use the definition of Expectation. And partition (0,∞) into intervals (0,t) and (t,∞). :)