GATE CSE
First time here? Checkout the FAQ!
x
0 votes
78 views

asked in Probability by Veteran (20.2k points)   | 78 views

2 Answers

+1 vote
Best answer
a. for value of k, it seems its a continuous PDF, so we know one thing about PDF as,

    $\int_{0}^{infinite} PDF = 1$

   but here PDF is divided in intervals,so

    $\int_{0}^{6}kx2 + \int_{6}^{12} k(12-x)^{2} = 1$

    solve it you will get k = $\frac{1}{144}$

b.  probability of storm duration > 8hr

     in this case our range would be    8 <= x <= 12

     p = $\int_{8}^{12} \frac{1}{144} (12-x)^{2}$

    solving this gives, p = 4/27....(i m not sure, please cross check)

c. in this case probability we have to find in interval 5 to 7 which is divided in two interval by 6

    so our 2 intervals would be  5 to 6, and 6 to 7

   p = $\int_{5}^{6} \frac{1}{144} x^{2} + \int_{6}^{7} \frac{1}{144} (12-x)^{2}$

   solve it you will get, p = $\frac{91}{ 3 * 144}$ ..... please cross check
answered by Loyal (3.1k points)  
selected by
+1 vote

 

 

This solves the first part of ques. I hope u can solve the second one too. 

 

answered by Loyal (3.6k points)  
Top Users Feb 2017
  1. Arjun

    5386 Points

  2. Bikram

    4230 Points

  3. Habibkhan

    3952 Points

  4. Aboveallplayer

    3086 Points

  5. Debashish Deka

    2564 Points

  6. sriv_shubham

    2318 Points

  7. Smriti012

    2236 Points

  8. Arnabi

    2008 Points

  9. mcjoshi

    1696 Points

  10. sh!va

    1684 Points

Monthly Topper: Rs. 500 gift card

20,863 questions
26,021 answers
59,689 comments
22,131 users