Ask Questions, Get Answers
Menu
X
JEEMAIN Crash Practice
15 Test Series
NEET Crash Practice
5 Test Series
CBSE XII
Math
JEEMAIN
Math
Physics
Chemistry
Practice Test Series
CBSE XI
Math
NEET
Physics
Chemistry
Biology - XII
Biology - XI
Olympiad class V
Math - 5 Test Series
Olympiad class VI
Math - 5 Test Series
studyplans
JEEMAIN Crash Practice
15 Test Series
NEET Crash Practice
5 Test Series
CBSE XII
Math
JEEMAIN
Math
Physics
Chemistry
Practice Test Series
CBSE XI
Math
NEET
Physics
Chemistry
Biology - XII
Biology - XI
Olympiad class V
Math - 5 Test Series
Olympiad class VI
Math - 5 Test Series
mobile
exams
ask
sample papers
tutors
pricing
sign-in
Download our FREE mobile app with 1000+ tests for CBSE, JEE MAIN, NEET
X
Search
Topics
Want to ask us a question?
Click here
Browse Questions
Student Questions
Ad
Home
>>
TN XII Math
>>
Probability Distribution
0
votes
Let $X$ have a poisson distribution with mean $4$.Find $(i) \;P(X\leq $3$)\qquad[e^{-4} = 0.0183].$
tnstate
class12
bookproblem
ch10
sec-1
exercise10-4
p218
q1
q1-1
Share
asked
Apr 21, 2013
by
poojasapani_1
edited
Sep 18, 2013
by
sreemathi.v
Please
log in
or
register
to add a comment.
Can you answer this question?
Do not ask me again to answer questions
Please
log in
or
register
to answer this question.
1 Answer
0
votes
Toolbox:
A random variable $X$ is said to have a poisson distribution of the probability mass function of $X$ is
$P(X=x)=\large\frac{e^{-\lambda }\lambda^x}{x!}$$\qquad (x=0,1,2........$ for some $\lambda > 0)$
Constants of a poisson distribution : Mean=Variance=$\lambda$
A continuous random variable $X$ is said to follow a normal distribution with parameter $\mu$ and $\sigma$ (or $\mu$ and $\sigma^2$) if the probability density function is
$f(x)=\large\frac{1}{\sigma \sqrt{2\pi}}$$e^{-\large\frac{1}{2}(\frac{x-\mu}{\sigma})^2};-\infty < x < \infty,-\infty< \mu <0$ and $\sigma > 0$
$X\sim N(\mu,\sigma)$
Constants of a normal distribution :
Mean =$\mu$,variance =$\sigma^2$,standard deviation =$\sigma$
Step 1:
$X\sim P(4)$
$\therefore P(X=x)=\large\frac{e^{\Large -4}4^{\Large x}}{x!}$$\qquad x=0,1,2....$
Step 2:
$P(X\leq 3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)$
$\qquad\qquad=e^{\Large -4}\big[\large\frac{4^0}{0!}+\frac{4^1}{1!}+\frac{4^2}{2!}+\frac{4^3}{3!}\big]$
$\qquad\qquad=0.0183\big[\large\frac{(1+4+8)3+32)}{3}\big]$
$\qquad\qquad=0.0061[71]$
$\qquad\qquad=0.4331$
answered
Sep 18, 2013
by
sreemathi.v
Please
log in
or
register
to add a comment.
Related questions
0
votes
1
answer
Let $x$ have a poisson distribution with mean $4$.Find$P(2\leq$X$<$5$)[e^{-4}=0.0183].$
asked
Apr 21, 2013
by
poojasapani_1
tnstate
class12
bookproblem
ch10
sec-1
exercise10-4
p218
q1
q1-2
0
votes
1
answer
If the probability of a defective fuse from a manufactuning unit is $2\%$ in a box of $200$ fuses find the probability that more than $3$ fuses are defective$ [e^{-4}=0.0183].$
asked
Apr 21, 2013
by
poojasapani_1
tnstate
class12
bookproblem
ch10
sec-1
exercise10-4
p218
q2
q2-2
0
votes
1
answer
The number of accidents in a year involving taxi drivers in a city follows a poisson distribution with mean equal to $3$ out of $1000$ taxi drivers find approximately the number of driver with more than $3$ accidents in a year $[e^{-3}=0.0498].$
asked
Apr 21, 2013
by
poojasapani_1
tnstate
class12
bookproblem
ch10
sec-1
exercise10-4
p219
q5
q5-2
modelpaper
jun-2006
oct-2008
oct-2009
0
votes
1
answer
The number of accidents in a year involving taxi drivers in a city follows a poisson distribution with mean equal to $3$. Out of $1000$ taxi drivers find approximately the number of driver with no accident in a year .$[e^{-3} = 0.0498].$
asked
Apr 21, 2013
by
poojasapani_1
tnstate
class12
bookproblem
ch10
sec-1
exercise10-4
p219
q5
q5-1
modelpaper
jun-2006
oct-2008
oct-2009
0
votes
1
answer
If the probability of a defective fuse from a manufactuning unit is $2\%$ in a box of $200$ fuses find the probability that exactly $4$ fuses are defective
asked
Apr 21, 2013
by
poojasapani_1
tnstate
class12
bookproblem
ch10
sec-1
exercise10-4
p218
q2
q2-1
0
votes
1
answer
Alpha particles are emitted by a radio active source at an average rate of $5$ in a $20$ minutes interval.Using poisson distribution find the probability that there will be at least $2$ emission in a particular $20$ minutes interval .$[e^{-5}=0.0067].$
asked
Apr 21, 2013
by
poojasapani_1
tnstate
class12
bookproblem
ch10
sec-1
exercise10-4
p219
q4
q4-2
0
votes
1
answer
Alpha particles are emitted by a radio active source at an average rate of $5$ in a $20$ minutes interval.Using poisson distribution find the probability that there will be $2$ emission.$[e^{-5}=0.0067].$
asked
Apr 21, 2013
by
poojasapani_1
tnstate
bookproblem
ch10
sec-1
exercise10-4
p219
q4
q4-1
Ask Question
Tag:
Math
Phy
Chem
Bio
Other
SUBMIT QUESTION
►
Please Wait
Take Test
JEEMAIN Crash Practice
15 Test Series
NEET Crash Practice
5 Test Series
JEEMAIN
350+ TESTS
NEET
320+ TESTS
CBSE XI MATH
50+ TESTS
CBSE XII MATH
80+ TESTS
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...