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##################### Problem -1 #######################

Mr. Rahman, Prof of the ICE department, PUST is interested in studying which Blood type is most common. He asked his statistics students to state their blood types. The response of 40 students was to state their blood types. The responses of 40 students in the class are given below. O, A, B, AB, O, A, O, B, AB, B, O, A, A, B, O, B, A, AB, O, AB, A, O, O, A, B, B, A, O, AB, O, A, O, O, A, B, O, O, B, AB, B

• I. Construct a frequency distribution table and relative frequency distribution of the data.
• II. Plot the data bar chart and pie chart.
• III. Comment on the data set.

############### Problem-2 ################

The table below displays the number of days to maturity for 40 short-term investments. The data are from BARRON’s magazine. Using limit grouping organize the data into frequency and relative frequency distribution. 70,64,99,55,64,89,87,65,62,38,67,70,60,69,78,39,75,56,71,51,99,68,95,86,57,53,47, 50,55,81,80,98,51,36,63,66,85,79,83,70.

• i. Construct a frequency distribution table.
• ii. Plot histogram of this frequency.
• iii.Find mean, variance, standard deviation, quantile, mode, boxplot, summary.
• iv. Find mean deviation (Mean), mean deviation (Median), and mean deviation (Mode).
• v. Find the coefficient of variance, kurtosis, and skewness.

############### Problem-3 ###########

A fair coin is tossed three times.

• I. Make the sample space.
• II. Make an event in which Head appears in the first toss and another event in which Head appears in the third toss.
• III.Intersect and union these two events.
• IV. Make probability space for this event.
• V. Calculate the probability of the event in which Head appears in the first toss.

############### Problem-4 #############

A balanced die is thrown two times.

• I. Make sample and probability space.
• II. Calculate the probability of throwing the same number.
• III. What is the probability that the sum is greater than or equal to 4?
• IV. Given that the sum is greater than or equal to 4, find the probability of throwing the same number.

########## Problem-5 #########

A balanced die is thrown three times.

• I. Find the probability of a random variable X=X1+X2-X3.
• II. Find the probability of a random variable X>4.
• III. Find a random variable that finds the maximum among X1, X2 and X3

############## Problem-6 ###############

Given the following data: 0,1,2,3,4,5 and n=5, p=0.45

• I. Calculate binomial distribution and make a bar plot.
• II. Calculate Pr(X<=2) in binomial distribution.
• III.Calculate Pr(X>=3)
• IV. Calculate Pr(X=2)
• V. Calculate Pr(1<X<=3)
• VI. Find the cdf of the data.