Questions related to Statistics I - Hamro CSIT

Write notes on any two:

Nominal and ordinal scale

Kurtosis

Five number summary

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

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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?

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If X and Y are two random variables having joint density function:

∫(X, Y) = 1/8 (6 – x – y), 0 < x < 2, 2 < y < 4

= 0, otherwise

Find P(X < 1.5 and 1 < Y < 3)

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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.

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A coin is tossed two times and if X denotes the number of heads obtained, find (i) E(x) (ii) E(X²) (iii) V(X) (iv) E(2X² + 3x – 5)

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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.

Show that the probability of being defective is 0.0315

Given that it is defective, find the probability that was produced on machine M1.

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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) non of them solve the problem (ii) the problem will be solved.

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Two batsmen A and B made the following runs in a series of cricket matches.

A 10 0 56 80 24

B 36 37 45 28 29

Who is a more consistent player, and why?

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The following table shows the marks obtained by 130 students in computer science.

Marks less than 40 40-50 50-60 60-70 70-80 80 or above

No. of students 14 24 36 25 20 11

Find the appropriate measure of central tendency.

Compute the minimum marks obtained by the top 20% of students.

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