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Edps 590BAY Fall 2019 C.J.Anderson Homework 1 Answers ..., Study notes of Probability and Statistics

Texas A&M University (A&M)Probability and Statistics

Elvis Presley had a twin brother (who died at birth). What is the probability that Elvis was an identical twin? (approximate the probability of a boy or girl = ...

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Edps 590BAY
Fall 2019
C.J.Anderson
Homework 1
Answers
1. The name of R for release 5.6.1 is “ ”.
2. (From Gelman) Conditional Probability: Approximately 1/125 of all
births are fraternal twins and 1/300 of births are identical twins.
Elvis Presley had a twin brother (who died at birth). What is the
probability that Elvis was an identical twin? (approximate the
probability of a boy or girl = 1/2).
Given:
Elvis’s twin is a boy
P(Girl) = P(Boy) = 1/2
P(identical) = (1/300)
P(fraternal) = (1/125)
Can Find:
Since we know that for identical twins, the siblings are either both are
boys or both are girls,
P(brother & identical) = P(brother|identical)P(identical) = (1/2)(1/300)
Since we know that for fraternal twins, they can be both boys, boy
girls, boy(first born)-girl(second born), or girl(first born)-boy(second
born), then there is only 1 out of 4 ways to have two boys,
P(brother & fraternal) = P(brother|fraternal)P(fraternal) = (1/4)(1/125)
1
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Edps 590BAY Fall 2019 C.J.Anderson

Homework 1 Answers

  1. The name of R for release 5.6.1 is “ ”.
  2. (From Gelman) Conditional Probability: Approximately 1/125 of all births are fraternal twins and 1/300 of births are identical twins. Elvis Presley had a twin brother (who died at birth). What is the probability that Elvis was an identical twin? (approximate the probability of a boy or girl = 1/2). Given:

Elvis’s twin is a boy

P (Girl) = P (Boy) = 1/ 2 P (identical) = (1/300) P (fraternal) = (1/125) Can Find:

Since we know that for identical twins, the siblings are either both are boys or both are girls,

P (brother & identical) = P (brother|identical)P (identical) = (1/2)(1/300)

Since we know that for fraternal twins, they can be both boys, boy girls, boy(first born)-girl(second born), or girl(first born)-boy(second born), then there is only 1 out of 4 ways to have two boys,

P (brother & fraternal) = P (brother|fraternal)P (fraternal) = (1/4)(1/125)

P (twin is a brother) = P (brother & identical) + P (both boys & fraternal) = P (brother|identical)P (identical + P (brother|fraternal)P (fratern = (1/2)(1/300) + (1/4)(1/125) = .0036¯ 6

Answer:

P (identical twin|brother) =

P (brother & identical) P (twin brother)

=

From google search,

On January 8, 1935, Elvis Aron (later spelled Aaron) Presley was born at his parents’ two-room house in East Tupelo, Mississippi, about 35 minutes after his identical twin brother, Jesse Garon, who was stillborn. The next day, Jesse was buried in an unmarked grave in nearby Priceville Cemetery.Jan 8, 2019.

  1. Mathematical Models of Probabilities: Kruschke page 31, exercise 2. Given: - 4 sided die with x = 1,2, 3, or 4 (number of dots) - Model A: p(x) = 1/ - Model B: p(x)=x/ - Model C: p(x)= 12/(25x)