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Statistics Week 12 Graded Assignments IIT Madras

by Khushi Dii
August 15, 2023August 20, 2023
Foundation Graded Assignments

Statistics week 12 graded assignment Complete Solutions Are Discussed In This Blog We Hope This Might Help You All In Matching Answers . Or For Some Others Reasons Not Able To Complete Graded Assignments

Let a random variable is uniformly distributed over

[a, b]

with expectation and variance

9.5

and

12 81

respectively. Find the value of

ab

1 point

Probability density function of a random variable

X

is given by:

f (x)

{k x^{2} 0 if x \in [0,1] otherwise

Find

P (0.2 < X < 0.8)

?
Hint:

\int_{a}^{b} c x^{2} d x = c 3 b ^{3} - a ^{3}

where,

c

is a constant.

9 0. 8 ^{3} - 0. 2 ^{3}

9 0. 8 ^{2} - 0. 2 ^{2}

0. 8^{2} - 0. 2^{2}

0. 8^{3} - 0. 2^{3}

The amount of milk produced every day by a dairy is uniformly distributed between

100

litres and

120

litres. What is the probability that the amount of milk produced is more than

118

litres given that on that day, more than

109

litres of milk was produced? (Enter the answer correct to 2 decimal place)

1 point

The time that Jan shatabdi express will reach the Delhi station is uniformly distributed between

3

p.m and

7

p.m. What is the probability that the train reaches Delhi exactly at

6

p.m?

1 point

The length of time for one person to be served at a restaurant is exponentially distributed with an expected time of

5

minutes. If

5

persons arrived at the restaurant then what is the probability that at least

2

of them will be served in more than

7

minutes? (Assume that each person is served independently)

1 - (1 - e^{- 35})^{5} - [5 e^{- 35} (1 - e^{- 35})^{4}]

1 - (e^{- 1.4})^{5} - [5 (e^{- 1.4})^{4} (1 - e^{- 1.4})]

1 - (e^{- 35})^{5} - [5 (e^{- 35})^{4} (1 - e^{- 35})]

1 - (1 - e^{- 1.4})^{5} - [5 e^{- 1.4} (1 - e^{- 1.4})^{4}]

Probability density function of a random variable

X

is given by

f (x) = ⎩ ⎨ ⎧ 0.2 x 0.2 0.2 x - 0.2 0.4 0 if 0 \leq x \leq 1 if 1 \leq x \leq 2 if 2 \leq x \leq 3 if 3 \leq x \leq 4 otherwise

Find the probability that

0 < x < 2.5

. (Answer upto three decimal points)

Hint : Try to find the area under pdf using integration, otherwise draw the graph of pdf of

X

1 point

In a certain exhibition, the time for the next visitor to come is exponentially distributed with a standard deviation of

11

minutes. What will be the expected time (in minutes) for two visitors to arrive if one comes after the other? (Note that the arrival of a visitor is independent of the arrival of the previous visitor.)

11 1

11 2

2 \times 11

The total duration (in minutes) of a badminton match in the Premier Badminton League (PBL) is uniformly distributed between

[a, b]

with variance

12

square minutes. The probability that a match will last at most

45

minutes is

6 1

. Find the expected time duration (in minutes) of a badminton match. (Enter the answer correct to 1 decimal place)

1 point

The probability density function of the time

X

(in minutes) between calls at the customer care is given by:

f (x)

⎩ ⎨ ⎧ 9 1 e^{9 - x} 0 if x > 0 otherwise

Find the probability that time between calls exceeds the mean time.

e 1

e

1 - e 1

1 - e

1 point

The lifetime of a light bulb is exponentially distributed with a mean life of

19

months. If there are

50

% chances that a light bulb will last at most

t

months, then what is the value of

t

19 \times ln (100 100 - 50)

19 1 ln (100 100 - 50)

19 1 ln (100 - 50 100)

19 \times ln (100 - 50 100)

Tags:Week 12 Graded Assignments

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