Preyom C INFR 1400 Assignmetn 1

Preyom Choudhury 100783615 1. [6 marks] Suppose you are given the following set of 28 observation values: 45, 50, 55, 60, 65, 70, 75, 75, 80, 80, 80, 80, 85, 85, 85, 85, 85, 85, 90, 90, 90, 90, 90, 90, 90, 90, 95, 100 Calculate the (a) mean, (b) median, (c) variance, (d) standard deviation, (e) Q1 (the first quartile or 25 th percentile), (f) Q3 (the third quartile or the 75 th percentile). Sum of all values:2240 Number of Values: 28 a) x = x 1 + x 2 + x 3 + ... + x n n x = x 1 + x 2 + x 3 + ... + x 28 28 x = 45 + 50 + 55 + ... + 100 28 x = 2240 28 x = 80 The value of the mean ( x ) is 80 b) 85 + 85 2 = 85 The median is 85 c) x i − x ¿ ¿ ¿ 2 ¿ ∑ i = 1 n ¿ S 2 = ¿

Preyom Choudhury 100783615 45 − 80 ¿ ¿ 50 − 80 ¿ ¿ 100 − 80 ¿ ¿ ¿ 2 ¿ S 2 = ¿ S 2 = 5100 27 S 2 = 188.8888889 S 2 = 188.89 The Varience is 188.89 d) s = √ ❑ s = √ ❑ s = 13.74372589 s = 13.74 e) Q1 = 75 f) Q3 = 90

Preyom Choudhury 100783615 2. [5 marks] About 30% of human twins are identical, and the rest are fraternal. Identical twins are necessarily the same sex, half are males and the other half are females. One- quarter of fraternal twins are both male, one-quarter both female, and one-half are mixes: one male, one female. You have just become a parent of twins and are told they are both girls. Given this information, what is the probability that they are identical? The probability of the twins being identical is 30% or P(I) = 0.3 The probability of the twins being identical and same sex (female) is 50% or P(FF|I) = 0.5 The probability of the twins being identical and same sex (male) is 50% or P(MM|I) = 0.5 Let A be the vent that they are fraternal twins The probability of the twins being fraternalis 70% or P(A) = 0.7 The probability of the twins being fraternal and being different sex is 50% or P(MF|A) = 0.5 The probability of the twins being fraternal and same sex (male) is 25% or P(MM|A) = 0.25 The probability of the twins being fraternal and same sex (femal) is 25% or P(FF|A) = 0.25 The required probability is P ( I ∨ FF )= P ( FF ∨ I ) × P ( I ) P ( FF ) Must find P(FF) P ( FF )= P ( FF ∨ I ) ×P ( I )+ P ( FF ∨ A ) ×P ( A ) ¿ 0.5 × 0.3 + 0.25 × 0.7 ¿ 0.325 P ( I ∨ FF )= 0.5 × 0.3 0.325 P ( I ∨ FF )= 0.461 The probability of the twins being identical given that they are both girls is 0.461