Elements of Statistics & Probability Assignment 3-5

STA201: Elements of Statistics & Probability
Assignment 3-5
 Marks = 30 + 3
1. (a) In a simultaneous throw of a pair of fair 6-sided dice, find the probability of getting:
(i) A sum of 8
(ii) A doublet (two dice landing on the same value)
(iii)A sum greater than 5
(iv)An odd number on one and an even number on the other
(b) A bag contains 30 balls numbered 1 through 30. Suppose drawing an even numbered ball
is considered a ‘Success’. Two balls are drawn from the bag with replacement. Find the
probability of getting:
(i) Two successes
(ii) Exactly one success
(iii) At least one success
(iv) No successes
2. There are three coins in a box. One is a two-headed coin, another is a fair coin, and the third
is a biased coin that comes up heads 75 percent of the time. When one of the three coins is
selected at random and flipped, it shows heads. What is the probability that it was the twoheaded coin?
3. Assume that the chances of a patient suffering from high blood pressure is 60%. It is also
assumed that a course of meditation reduces the risk of high blood pressure by 45% and
prescription of certain drugs reduces its chances by 55%. At a time, a patient can choose any
one of the two options with equal probabilities. It is given that after going through one of the
two options, the patient selected at random does not suffer from high blood pressure. Find the
probability that the patient chose a course of meditation?
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STA201 (Elements of Statistics & Probability) _Assignment 3-5_Summer 2022
4. When traveling from Bangladesh to Vietnam, travelers need to first land at Kuala Lumpur,
and then get on a connecting flight to Vietnam. The total time in transit Y in hours can be
shown to have the following:
(i) What is the probability that total transit time is at most 6 hours?
(ii) What is the probability that the transit time is either less than 3 hours or more than 7 hours?
(iii) What is the expected total transit time for travelers going from Bangladesh to Vietnam?
(iv) Determine the standard deviation in the total transit time.
5. In each of 4 races, the Democrats have a 60% chance of winning. Assuming that the races are
independent of each other, what is the probability that:
(i) The Democrats will win 0 races, 1 race, 2 races, 3 races, or all 4 races?
(ii) The Democrats will win at least 1 race.
(iii) The Democrats will win a majority of the races.
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STA201 (Elements of Statistics & Probability) _Assignment 3-5_Summer 2022
BONUS ASSIGNMENT
Use built-in R functions to solve the following problems- Marks-3.0
Q1. Create the following vector90, 178, 547, 453, 189, 377, 264, 333, 289, 391, 320, 300,210, 310, 121, 154, 248, 292,
368, 423
(i) Find mean, median, standard deviation of the above values (from question 1)
(ii) Find square root of all values
(iii) Sort the values
(iv) Find the length of the vector
(v) Find summation and product of all values
Q2. Create the following data frameNumber of Rooms kwh
12 9
9 7
14 10
6 5
10 8
(i) Find Pearson’s correlation coefficient between two variables (Number of rooms &
KWH)
(ii) Estimate the regression coefficients of a regression of KWH on Number of rooms.
(iii) Plot a scatter diagram of KWH against Number of rooms
Submission Guideline: Submit the code and output along with the assignment
solutions at the end (hard/ soft copy). This will be counted as a bonus. Take help
from R- tutorials shared with you.