JNTU
JNTU MCA 2021 PROBABILITY AND STATISTICS Previous Question Paper (July/August - 2021 - R17)
Answer any five questions. All questions carry equal marks.
Main
Two digits are selected at random from the digits 1 through 9.
i) If the sum is odd, what is the probability that 2 is one of the digit selected.
ii) If 2 is one of the digits selected, what is the probability that the sum is odd?
Answer
The total number of ways to select 2 distinct digits from 9 is 9C2 = 36. Let the set of digits be S = {1, 2, 3, 4, 5, 6, 7, 8, 9}. A sum is odd if one digit is even and one is odd. There are 4 even digits {2, 4, 6, 8} and 5 odd digits {1, 3, 5, 7, 9}. The number of ways to get an odd sum is 4 × 5 = 20.
i) Let A be the event that the sum is odd and B be the event that 2 is selected. The number of ways to select two digits such that 2 is one of them and the sum is odd requires picking 2 (even) and one odd digit. There are 5 such pairs: (2,1), (2,3), (2,5), (2,7), (2,9). Thus, P(B|A) = n(A ∩ B) / n(A) = 5 / 20 = 1/4.
ii) The event B (2 is selected) consists of 8 pairs: (2,1), (2,3), (2,4), (2,5), (2,6), (2,7), (2,8), (2,9). Out of these, the pairs with an odd sum are (2,1), (2,3), (2,5), (2,7), (2,9), which are 5 pairs. Thus, P(A|B) = n(A ∩ B) / n(B) = 5 / 8.
A fair coin is tossed until a head or five tails occurs. Find the expected number of tosses of the coin.
Answer
Let X be the number of tosses. The experiment stops when a Head (H) appears or 5 Tails (T) occur. The possible outcomes and their probabilities are:
- X=1: {H}, P(X=1) = 1/2
- X=2: {TH}, P(X=2) = (1/2)2 = 1/4
- X=3: {TTH}, P(X=3) = (1/2)3 = 1/8
- X=4: {TTTH}, P(X=4) = (1/2)4 = 1/16
- X=5: {TTTTH, TTTTT}, P(X=5) = (1/2)5 + (1/2)5 = 1/32 + 1/32 = 2/32 = 1/16
The expected value E[X] is calculated as:
State and prove Boole’s inequalities.
Answer
Sign in to view the complete answer paper.
A, B, C in order toss a coin. The first one to toss head wins the game. What are the probabilities of winning, assuming that the game may continue indefinitely?
Answer
Sign in to view the complete answer paper.
A continuous random variable X has the probability density function:
Find the cumulative distribution function for X. Also find P(1/4 < X ≤ 3/4) and P(X < 1/2).
Answer
Sign in to view the complete answer paper.
Find the probability of getting 1 or 4 or 5 or 6 in throwing a die 5 to 7 times among 9 trials using normal distribution.
Answer
Sign in to view the complete answer paper.
Show that for normal distribution the quartile deviation, mean deviation and standard deviation are approximately 10:12:15.
Answer
Sign in to view the complete answer paper.
Determine the mean and standard deviation of the sampling distribution of means of 300 random samples each of size 36 are drawn from a population of size 1500 which is normally distributed with mean 22.4 and standard deviation 0.048, if sampling is done i) with replacement and ii) without replacement.
Answer
Sign in to view the complete answer paper.
Construct 95% confidence interval for the true proportion of computer literates if 47 out of 150 persons from rural areas are computer literates.
Answer
Sign in to view the complete answer paper.
A normal population has a mean 0.1 and a standard deviation of 2.1. Find the probability that the mean of simple sample of 900 members will be negative.
Answer
Sign in to view the complete answer paper.
In a study conducted for 500 days, only on 4 days it was recorded that ‘lead’ content in a famous river exceeded 200mg/cm. Construct an upper 99% confidence limit for the probability that the ‘lead’ content in the river will exceed 200mg/cm on any one day.
Answer
Sign in to view the complete answer paper.
A briefcase manufacturing company claims that 80% of executives carried briefcases produced by them. Verify its claims if in a random sample of 900 executives, 675 used the company’s briefcases. Use 5% level of significance.
Answer
Sign in to view the complete answer paper.
Explain, stating clearly the assumptions involved, the t-test for testing the significance of the difference between the two sample means.
Answer
Sign in to view the complete answer paper.
The tangent of the angle between two regression lines is 0.6 and if σx = 1/2 σy, find the correlation coefficient between x and y.
Answer
Sign in to view the complete answer paper.