KTU B.Tech Important S4 Question Papers For Probability Distributions,Transforms And Numerical Methods [ PDTM ] MA202 | Question Bank


KTU B.Tech Important S4 Question Papers For Probability Distributions,Transforms And Numerical Methods

KTU B.Tech Important S4 Question Papers For Probability Distributions,Transforms And Numerical Methods [ PDTM ] MA202 | Question Bank

Module I And II

1) A box contains 100 cellphones, 20 of which are defective. 10 cellphones are selected for inspection. Find the probability that

(i) at least one is defective

(ii) at most 3 are defective

(iii) all the 10 are defective

iv) none of the 10 is defective.

2) A discrete random variable X has the following probability distribution.


x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8


p(x) | k | 3k | 5k | 7k | 9k | 11k | 13k | 15k | 17k

Find

i) The value of k.

ii) P(X < 4)

iii) P(X > 5)

3) A random variable X has the following probability distribution.


x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7

p(x) | 0 k | 2k | 2k | 3k | k^2 | 2 k^2 | 7 k^2 +k

Find

iii) The value of k.

iv) P(X > 2)

v) P(X ≤ 4)

vi) P(1.5 < X < 4.5 / X > 2)
4) The actual amount of instant coffee that a filling machine puts in to “4”ounce jars may be looked upon as a random variable having a normal distribution with σ = 0.04 ounce. 

If only 2% of the jars are to contain less than 4 ounces, what should be the mean fill of these jars.

5) In a certain city, the number of power outages per month is a random variable having a distribution with =11.6 and σ = 3.3. 

If this distribution can be approximated closely with a normal distribution.

What is the probability that there will be at least 8 outages in any one month

6) In a certain experiment the error made in determining the solubility of a substance is a random variable having uniform distribution with = -0.025 and = 0.025. 

What are the probabilities that such an error will be between a) 0.010 and 0.015 b) -0.012 and 0.012

7) It is known that 5% of the books bound at a certain bindery have defective bindings. Find the probability that 2 of 100 books bound by this bindery will have defective binding using

(i) The formula for the binomial distribution

(ii) The Poisson approximation to binomial distribution.
8) The monthly breakdowns of a computer is a random variable having Poisson distribution with mean equal to 1.8. 

Find the probability that this computer will function for a month

(i) Without a breakdown

(ii) With only one breakdown

(iii)With at least one breakdown.

9) Derive the mean and variance of Binomial Distribution.

10) Derive the mean and variance of Uniform Distribution.

11) Derive the mean and variance of Poisson Distribution.


12) If a random variable has the probability density
Find the probabilities that it will take on a value.

i) Between 1 and 3.

ii) Greater than 0.5

iii) Find the mean and variance of X

13) Find such that the following can serve as the probability density of a random variable
14) In an intelligence test administered on 1000 children, the average was 60 and standard deviation was 20. 

Assuming that the marks obtained by the children follow normal distribution, find the number of children who have scored

i) Over 90 marks

ii)Below 40 marks


iii) Between 50 and 80 marks.

15) The number of personal computers sold daily at CompuWorld is uniformly distributed with minimum of 2000 PCs and maximum of 5000 PCs. What is the probability that

(i) The daily sales will fall between 2500 and 3000 PCs

(ii) CompuWorld will sell at least 4000 PCs

(iii) CompuWorld will exactly sell 2500 PCs.

16) The time (in hours) required to repair a machine is exponentially distributed with parameter lamda = 1/3.What is the probability that the repair time exceeds 3 hours?

17) An electrical firm manufactures light bulbs that have life, before burn-out, that is normally distributed with mean equal to 800 hours and a standard deviation of 40 hours. Find the probability that a bulb burns

i) More than 834 hours

ii) Between 778 and 834 hours
18) In a normal distribution, 31% of the items are under 45 and 8% are over 64. Find the mean and standard deviation of the distribution.

19) After a large number of assays of the gold content in rocks collected from an open pit mine,a mining engineer postulates that the natural log of the gold content (oz/st) follows a normal distribution with mean -4.6 and variance 1.21.Under this distribution, would it be unusual to get 0.0015 oz/st gold or less in an assay.

20) In a continuous distribution , the probability density is given by f(x)= kx(2-x), 0<x<2. Find the value of k, mean, variance and distribution function.

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