No The disease depends on mothers attributes If the elder child has the disease

No the disease depends on mothers attributes if the

This preview shows page 4 - 5 out of 5 pages.

No. The disease depends on mother’s attributes. If the elder child has the disease then the mother must have the disease as it can be passed only through the mother having the disease and hence the younger child is more likely to get the disease. c. The elder child is found not to have the disease. A week later, the younger child is also found not to have the disease. Given this information, find the probability that the mother has the disease. P ( neither child hasdisease )= 3 / 4 M | C 1 ' ∩ C 2 ' ) = P ( M ∩ ( C 1 ' ∩ C 2 ' ) ) P ( C 1 ' ∩C 2 ' ) = P ( C 1 ' ∩C 2 ' M ) ∙ P ( M ) P ( C 1 ' ∩C 2 ' ) = P ( C 1 ' M ) ∙ P ( C 2 ' M ) ∙P ( M ) P ( C 1 ' ∩C 2 ' ) = ( 1 / P ( momhas disease neither childhas disease )= P ¿ 9. [5 marks] Let X be the number of heads in 10 fair coin tosses. a. Given that the first two tosses both land heads, find the probability that there were exactly 4 heads in the 10 coin tosses. P ( first twotossesareheads four heads | firsttwotosses are heads ¿ = P ( first twotossesare hea P ( first twotosses a b. Given that the first two tosses both land heads, what are the possible values of X? Is it a random variable? If yes, find the probability mass function. If no, why? Yes. X = number of total heads | first two tosses are heads P ( number of total heads firsttwotosses areheads )= ( 8 x 2 ) 2 8 for x = 2, 3, 4, …, 10.
Image of page 4
Total probability = 1 2 8 [ ( 8 0 ) + ( 8 1 ) + + ( 8 8 ) ] = 256 256 = 1 10. [5 marks] Suppose a fair die is tossed three times. Let X be the number of different faces that appear (so X = 1, 2, or 3). Find the pdf and cdf. X Outcomes Probability (pmf) Cdf 1 All three faces are the same 6 / 6 3 = 1/36 1 / 36 2 Exactly two faces are same ( 3 2 ) 6 5 6 3 = 15 / 36 16 / 36 3 All three faces are different 6 5 4 6 3 = 20 36 1 11. [3 marks] If X, Y, Z are events such that X and Y are independent and Y and Z are
Image of page 5

You've reached the end of your free preview.

Want to read all 5 pages?

  • Summer '18
  • Sagar Arora

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

Stuck? We have tutors online 24/7 who can help you get unstuck.
A+ icon
Ask Expert Tutors You can ask You can ask You can ask (will expire )
Answers in as fast as 15 minutes