What are the assumptions of Pearson's correlation? Bradford Electric Illuminating is studying the relationship between kilowatt-hours (thousands) used and the number of rooms in private single-family residences. A random sample of 5 houses yields the following. i. Find the correlation coefficient between the number of rooms and kilowatts-hours used. Interpret the result. ii. Determine the regression equation of kilowatts hours used on the number of rooms. Interpret the value of the regression coefficient. iii. Estimate the kilowatts-hours used for an 8 rooms house. [10]

What do you understand by measures of dispersion? What are the different measures of depression? The following table shows the data of time taken (in seconds) for completing each one of the series of 80 similar chemical experiments. Calculate mean time experiments, standard deviation, and variance and comment on your result. [10]

The following table shows the marks obtained by 130 students in computer science.i. Find the appropriate measure of central tendency. ii. Compute the minimum marks obtained by the top 20% of students. [5]

Two batsmen A and B made the following runs in a series of cricket matches. Who is a more consistent player, and why? [5]

Write notes on any two: i. Nominal and ordinal scale ii. Kurtosis iii. Five number summary [5]

Under what conditions Binomial distribution tends to Poisson distribution? The number of telephone calls received during the month of May is summarized in the following table. Fit the Poisson distribution. [10]

The mean and variance of the number of flights arriving late in a day are 2 and 1.6 respectively. Assuming binomial distribution, are those values consistent? If yes, find the probability that (i) none of the flights are late today and (ii) at least one flight is late today. [5]

What do you mean by normal distribution? From a batch of 10000, the lifetime of laptop batteries has a normal distribution with a mean of 40 months and a standard deviation of 8 months. What is the probability that a laptop selected at random will have life time (i) more than 50 months? (ii) between 40 and 50 months? [5]

Define conditional probability. A problem of statistics is given to three students, A, B, and C whose chances of solving the problem are in a ratio of 2:3:5. Find the probability that (i) none of them solve the problem (ii) the problem will be solved. [5]

A factory has three machines M1, M2, and M3 producing a large number of computer chips. Of the total daily production of items, 50% is produced on M1, 20% on M2, and 30% on M3. Records show that 4% of chips produced on M1 are defective, 2% produced of chips produced on M2 are defective and 2.5% of chips produced on M3 are defective. The occurrence of a defective chip is independent of all other chips. One chip is chosen at random from a day's total production. (i) Show that the probability of being defective is 0.0315 (ii) Given that it is defective, find the probability that was produced on machine M1. [5]

A coin is tossed two times and if X denotes the number of heads obtained, find (i) E(x) (ii) $E(x^2)$ (iii) $V(x)$ (iv) $E(2X^2 + 3x - 5)$ [5]

What do you understand by sampling? Differentiate between a simple random variable and stratified random sampling. [5]