Unit 8 - Week 6- Continuous Random Variables - Nptel

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18/05/2018 Probability Foundations for Electrical engineers - - Unit 8 - Week 6- Continuous Random Variables

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Unit 8 - Week 6-

Continuous Random Variables

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Course outline

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Week 0 - Experiments, sample space, events

Week 1 -

Probability space

Week 2 - Conditional probability

Week 3 - Independence

Week 4 - Discrete random variables

Week 5 - Conditional and joint

distributions, independence and

manipulations of random variables

Week 6- Continuous Random Variables

Real line as sample space Probability density function (pdf)

Cumulative distribution function (CDF) Continuous random variables

Due on 2018-03-23, 23:59 IST.

1 point 1)

1 point 2)

3)

Assignment 6

The due date for submitting this assignment has passed.

Submitted assignment

Which of the following could be modelled as a continuous random variables?

(1) The sum of numbers on a pair of two dice.

(2) The possible sets of outcomes from flipping six coins.

(3) The possible values of the temperature outside on any given day.

(1) only (3) only (1) and (3) (2) and (3)

No, the answer is incorrect.

Score: 0

Accepted Answers:

(3) only

A certain continuous random variable has a probability density function (PDF) given by:

Compute the value of using the properties of PDFs.

12 6 2 24

Score: 0

12

Suppose the amount of petrol sold daily at a service station is a continuous random variable uniformly distributed in the range litres to litres. The probability that the service station will sell exactly litres is _________________ .

Score: 0

(Type: Numeric) 0

f (x) = { Cx(1 − x)

²

0 : 0 ≤ x ≤ 1 : otherwise C

2000 5000

2500

(2)

Week 7- Joint distributions and transformations of random variables

Week 8 -

Expectations and Averages

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pdf and CDF of continuous random variables Spinning pointer example Important continuous distributions More continuous distributions Quiz : Assignment 6 Week 6 Feedback Week 6 Assignment Solution

1 point 4)

1 point 1 point 5)

1 point 6)

1 point 7)

8)

Buses arrive at ten-minute intervals starting at noon. A man arrives at the bus stop at a random time minutes after noon, where is uniformly distributed between and minutes. The probability that he waits a maximum of two minutes for a bus is ______________. Write your answer upto 3 decimal places.

Score: 0

(Type: Range) 0.198,0.202

A two-state traffic signal (for pedestrians) alternately shows Red for seconds and Green for seconds. Consider the time interval 0 to seconds in this problem. A jogger arrives at the signal at a uniformly random instant of time. Let denote the waiting time of the jogger at the signal, measured from the instant of arrival. Assume that the jogger can start and stop instantaneously. What is ?

0 0.2 0.25 0.75

Score: 0

0.2

Suppose a continous random variable is uniformily distributed between and . Find the probability that takes a value greater than ?

0.125 0.25 0.375 0.45

Score: 0

0.375

Which of the following is/are true of Gaussian distributions?

1. They are always symmetric about the mean.

2. The tail of Gaussian PDF decays faster than the tail of Cauchy PDF.

3. They always have a mean of 0.

1 and 2 only.

1,2 and 3.

1 only.

1 and 3 only.

Score: 0

1 and 2 only.

The lifetime of an alkaline battery is distributed as:

X X 0 60

= 8 T

R

= 2

T

G

10( T

R

+ T

G

) = 100

X P(X = 0)

N 690 850

N 790

X

(x) = { f

_λ

λe

^−λx

0 : x ≥ 0

: x < 0

(3)

1 point 1 point 9)

10)

1 point where per hour. The probability that the battery lasts for more than 20 hours is ____________.

Write your answer correct to three decimal places.

Score: 0

(Type: Range) 0.364,0.370

(True or False): Histograms are always defined over intervals of the form with because probabilities are always non-negative.

True False

Score: 0

False

Let be a Cauchy random variable with PDF . Compute . Write

your answer correct to 3 decimal places.

Score: 0

(Type: Range) 0.665,0.669

λ = 0.05

[a, b] a ≥ 0

X 1

π(1 + ) x

²

P(X > √ 3 ∣ X > 1)

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