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Miscellaneous 7 (II) · Q66

Q.Suppose error involved in making a certain measurement is continuous r.v. X with p.d.f. f

(x) = k (4 – x²) , for –2 ≤ x ≤ 2 and = 0 otherwise. Compute
(i) P ( X > 0)
(ii) P (–1 < x < 1)
(iii) P ( X < 0.5 or X > 0.5)
Maharashtra MsbshseTextbookSubjectiveImportance★★★★★
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As in Exercise 7.2 Q7, k=3/32k=3/32, so f(x)=332(4−x2)f(x)=\dfrac3{32}(4-x^2).

  1. By symmetry, P(X>0)=1/2P(X>0)=1/2.
  2. P(−1<x<1)=1116P(-1<x<1)=\dfrac{11}{16}.
  3. As printed, this condition is 'X < 0.5 OR X > 0.5', i.e. every real number except exactly X=0.5. For a continuous random variable a single point always has probability 0, so P(X=0.5)=0P(X=0.5)=0 and P(X<0.5 or X>0.5)=1−0=1P(X<0.5\text{ or }X>0.5)=1-0=1. (This differs from Exercise 7.2 Q7(iii), printed with a minus sign as '−0.5 < x or x > …

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