Complete the following table:

In a locality, 100 persons were randomly selected and asked about their educational achievements. The results were as follows:

Can we say that education depends on sex at 5% level of significance?

In a city, 36 out of a random sample of 500 men were found to drinkers at a certain date. After the heavy increase in tax on intoxicants, another sample of 100 men in the same city included 6 drinkers. Do you feel that the observed proportion of drinkers decreasing significantly at 1%level?

The following data relate to the number of items produced per shift followed normal distribution by two workers Rahul and Ramesh for a number of days:

Can it be inferred that Rahul is more stable worker compared to Ramesh by testing the variation in the item produced by them at 5% level of significance.

The blood cholesterol levels of a population of workers have mean 202 mg/dl and standard deviation 14 mg/dl. If a sample of 36 workers is selected from the population and sample mean is calculated then find

i) mean and standard error of the sampling distribution of the mean.

ii) approximate the probability that the sample mean of their blood cholesterol levels will lie between 198 mg/dl and 206 mg/dl.

A sample of 100 tyres is taken from a lot. The mean life of the tyres selected is the sample is found to be 40,000 kms with a standard deviation of 3200 kms. Is it reasonable to suppose the mean life of tyres in the lot as 41,000 kms at 5% level of significance? Also establish 95% confidence limits within which the mean life of tyres in the lot is expected to lie.

If the sample values are 3, 5, 2, 7, and 0 then obtain the ML estimate for parameter θ for the following distribution :

f(x, θ ) = θe^-θx; 0 ≤x, θ>0

A random sample of nine college students yielded the following data concerning the number of hours per day each student spent in using mobile phone:

5, 2, 7, 5.5, 3.5, 4, 5, 4.5, 4

Estimate the average number of hours per day spent in using mobile phone by the college students.

State whether the following statements are True or False. Give reason in support of your answer.
a) If probability density function of a t-distribution is

f(t) = 1/ π (1+t2) ; - ∞ <t< ∞
then degrees of freedom of the distribution will be 1.
b) If T1 and T2 are two estimators of an parameter θ such that Var(T1) = 1/2n and Var(T2) = 2/n then T1 is more efficient than T2.
c) If the probability of non rejection of H0 when H1 is true is 0.4 then power of the test will be 0.6.
d) The Wilcoxon signed-rank test is more powerful than the sign test.
e) The t-test is used for testing the independence of two attributes.

Events A, B, C are mutually exclusive and exhaustive. If odds against A are 4 :1and against B are 3: 2 . Find the odds against event C.

A person is known to hit the target in 3 out of 4 shots whereas another person is known to hit 2 out of 5 shots. Find the probability that the target being hit when they both try.

A die is rolled. If the outcome is a number greater than 2, what is the probability that it is an odd prime number?

If the probability that an individual suffers a bad reaction from an injection of a given  serum is 0.002, determine the probability that out of 400 individuals
(i) exactly 2
(ii) more than 3
(iii) at least one
 individuals suffer from bad reaction.

Comment on the statement: “The mean of a binomial distribution is 4 and variance 5”.

Let X and Y be two independent random variables such that X ~ B(5, 0.06) and Y ~ B(4, 0.6) . Find P[X+Y>1]

A player tosses two unbiased coins. He wins Rs. 10 if 2 heads appear, Rs. 5 if one head appears and Rs 1 if no head appears. Find the expected value of the amount won by him.

A rain coat dealer can earn Rs 800 per day during a rainy day. If it is a dry day, he can lose Rs 150 per day. What is his expectation, if the probability of rain is 0.6?

The following table represents the joint probability distribution of the discrete random variable (X, Y):

Find
a) The marginal distributions.
b) The conditional distribution of Y given X = 2

An insurance company insured 2000 scooter drivers, 3000 car drivers and 5000 truck drivers. The probabilities that scooter, car and truck drivers meet an accident are 0.02, 0.04, and 0.25 respectively. One of the insured persons meets with an accident. What is the probability that he is a
a) Scooter driver
b) Car driver

Determine the constant k such that the function f(x) = kx²(1-x)² , 0<x<1 2 is a beta distribution of first kind. Also, find its mean and variance.