5. 6. 7. 1. LONG QUESTIONS 2. 3. sample of 3 fuses are chosen at random drawing of which at most one fuse is defective 245 Vo +4G following ins:Mw replacement ii) With reache111 634 conditions: W 1. Two cards are drawn from a well-shuffled ordinary deck of 52 cards. Find the probabilit that they are both aces if the first card is (a) replaced (b) not replaced. A pair of dice is thrown. Let E be the event that the sum is greater than or equal to 10 an be the event that 5 appears on the first dice. Find P(E|F). Three urns contains 6 red, 4 black; 4 red, 6 black and 5 red, 5 black balls respectively of the urns is selected at random and a ball is drawn from it. If the ball drawn is red, find probability that it is drawn from the first urn. 2. 3. A bag contains 8 items of which 2 are defective. A man selects 3 items at random. Find the expected number of defective items he has drawn. A continuous random variable X has probability density function defined by : f(x) = {² (x + 1), for -1 < x < 1 0, otherwise of the random variable X. SHORT ANSWER TYPE MODULE-III A continuous random variable has the probability density function : (2e , x ≥ 0 -2x lo, otherwise than 0.5. ; Verify that f(x) is a density function also find the me f(x) = . Find the probabilities that it will take on a value: (i) between 1 and 3 (ii) great MODULE-IV If X be uniformly distributed in −2 ≤ x ≤ 2 .Find P(X < 1) and P(|x − 1| ≥ 1/ What is the probability mass function of Poisson distribution ? Let the cumulative distribution function of the random variable X is given by 0 x < 0
5. 6. 7. 1. LONG QUESTIONS 2. 3. sample of 3 fuses are chosen at random drawing of which at most one fuse is defective 245 Vo +4G following ins:Mw replacement ii) With reache111 634 conditions: W 1. Two cards are drawn from a well-shuffled ordinary deck of 52 cards. Find the probabilit that they are both aces if the first card is (a) replaced (b) not replaced. A pair of dice is thrown. Let E be the event that the sum is greater than or equal to 10 an be the event that 5 appears on the first dice. Find P(E|F). Three urns contains 6 red, 4 black; 4 red, 6 black and 5 red, 5 black balls respectively of the urns is selected at random and a ball is drawn from it. If the ball drawn is red, find probability that it is drawn from the first urn. 2. 3. A bag contains 8 items of which 2 are defective. A man selects 3 items at random. Find the expected number of defective items he has drawn. A continuous random variable X has probability density function defined by : f(x) = {² (x + 1), for -1 < x < 1 0, otherwise of the random variable X. SHORT ANSWER TYPE MODULE-III A continuous random variable has the probability density function : (2e , x ≥ 0 -2x lo, otherwise than 0.5. ; Verify that f(x) is a density function also find the me f(x) = . Find the probabilities that it will take on a value: (i) between 1 and 3 (ii) great MODULE-IV If X be uniformly distributed in −2 ≤ x ≤ 2 .Find P(X < 1) and P(|x − 1| ≥ 1/ What is the probability mass function of Poisson distribution ? Let the cumulative distribution function of the random variable X is given by 0 x < 0
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:sample of 3 fuses are chosen at random drawing of which at most one fuse is defective
245 Vo
4G
followhi donaIns:wal replacement ii) With&Rie replacenthel (63 ) 7
hcht:
Two cards are drawn from a well-shuffled ordinary deck of 52 cards . Find the probabili
that they are both aces if the first card is (a) replaced (b) not replaced .
A pair of dice is thrown. Let E be the event that the sum is greater than or equal to 10 an
be the event that 5 appears on the first dice . Find P(E|F) .
Three urns contains 6 red, 4 black; 4 red , 6 black and 5 red , 5 black balls respectively
5.
6.
7.
of the urns is selected at random and a ball is drawn from it. If the ball drawn is red, finc
probability that it is drawn from the first urn.
MODULE-III
LONG QUESTIONS
1.
A bag contains 8 items of which 2 are defective. A man selects 3 items at random. Find the
expected number of defective items he has drawn .
2.
A continuous random variable X has probability density function defined by :
(х + 1), for —1 <x<1
f(x) = {i
Verify that f(x) is a density function also find the me
0, otherwise
of the random variable X .
3.
A continuous random variable has the probability density function :
f(x) =
{2e-2x
lo, otherwise
than 0.5.
,x > 0
. Find the probabilities that it will take on a value: (i) between 1 and 3 (ii) great
MODULE-IV
SHORT ANSWER TYPE
1.
If X be uniformly distributed in -2 < x< 2 .Find P(X < 1) and P(\x – 1| 2;
2.
What is the probability mass function of Poisson distribution ?
3.
Let the cumulative distribution function of the random variable X is given by
0 ;
x < 0
0<x <;
F(X) =
Then P (x = ;)
1+x
sx<1
1;
x > 1
6/10
Find the value of c such that f(x) = {cx² ,0 < x < 3
0, otherwise
4.
is a dens.
GITA AUTONOMOUS COLLEGE,BHUBANESWAR
ENGINEERING MATHEMATICS-III
QUESTION BAN.
5.
Write the difference between probability function and probability distribution function .
6.
A fair coin is tossed 20 times what is the probability of getting at most 18 heads is
7.
In
distribution mean and variance are same
8.
What is Sampling. Write different types of Sampling .
9.
Write different characteristics of normal distribution .
10.
A fair coin is tossed 400 times. If X is the number of heads obtained, find the expected
value and variance of X.
11.
A book has four misprints per page(on average), what is the probability that a page
open at random will have no misprints on it.
MODULE-IV
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