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Probability Distribution

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JIMS Engineering Management Technical Campus
JIMS Engineering Management Technical Campus

Project by Ms.Mamta Barik Assistant Professor of JIMS management Technical Campus,Greater Noida. A probability distribution is a function that portrays the probability of acquiring the potential qualities that an irregular variable can assume. In other words the estimations of the variable fluctuate dependent on the hidden probability distribution.

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Presentation on PROBABILITY DISTRIBUTION Mamta Barik Applied Science Deptt. *Applied Mathematics-IV
* A probability distribution is a function that describes the likelihood of obtaining the possible values that a random variable can assume. In other words, the values of the variable vary based on the underlying is probability distribution. Binomial Poisson Normal They are of following types:
1.BINOMIAL DISTRIBUTION This distribution is based on Bernoullis trials. It is a discrete distribution. Its PDF is : P(x)= nCx px qn-x , 0<x<n where , n is total number of outcomes, x is possible number of outcomes, p is probability of success, q is probability of failure. Here, p+q=1 Mean=np Variance=npq
* Consider the following question:-
2. POISSON DISTRIBUTION It is a discrete distribution based on Bernoullis trials. It is a limiting case of binomial distribution. When n becomes very large and P becomes very small then Binomial distribution tends to Poisson distribution. Its PDF is: P(x) = e-了 了^x / x! ,0<x< * Poisson distribution has the following properties:- * Mean of the distribution = 了 . * Variance of the distribution = 了 .
* Consider the following question:-
3. NORMAL DISTRIBUTION It is a continuous probability distribution whose Probability Mass Function(PMF) is: P(x)= [1/ -<x< Its Mean= 亮 Variance= 2 Standard Deviation= It is a limiting case of Binomial distribution. When n becomes very large and P becomes close to 遜 then B.D tends to Normal distribution. 2]*e[(-1/2)(x-亮/)2]
3. NORMAL DISTRIBUTION It is a symmetrical distribution. In this, we convert x into z by the transformation: z= (x-亮)/ Total area under the normal curve is unity. P(-<z<)= 1 P(-<z<0)=P(0<z<)= 0.5 - z=0
* Consider the following question:-
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Probability Distribution

  • 1. Presentation on PROBABILITY DISTRIBUTION Mamta Barik Applied Science Deptt. *Applied Mathematics-IV
  • 2. * A probability distribution is a function that describes the likelihood of obtaining the possible values that a random variable can assume. In other words, the values of the variable vary based on the underlying is probability distribution. Binomial Poisson Normal They are of following types:
  • 3. 1.BINOMIAL DISTRIBUTION This distribution is based on Bernoullis trials. It is a discrete distribution. Its PDF is : P(x)= nCx px qn-x , 0<x<n where , n is total number of outcomes, x is possible number of outcomes, p is probability of success, q is probability of failure. Here, p+q=1 Mean=np Variance=npq
  • 4. * Consider the following question:-
  • 5. 2. POISSON DISTRIBUTION It is a discrete distribution based on Bernoullis trials. It is a limiting case of binomial distribution. When n becomes very large and P becomes very small then Binomial distribution tends to Poisson distribution. Its PDF is: P(x) = e-了 了^x / x! ,0<x< * Poisson distribution has the following properties:- * Mean of the distribution = 了 . * Variance of the distribution = 了 .
  • 6. * Consider the following question:-
  • 7. 3. NORMAL DISTRIBUTION It is a continuous probability distribution whose Probability Mass Function(PMF) is: P(x)= [1/ -<x< Its Mean= 亮 Variance= 2 Standard Deviation= It is a limiting case of Binomial distribution. When n becomes very large and P becomes close to 遜 then B.D tends to Normal distribution. 2]*e[(-1/2)(x-亮/)2]
  • 8. 3. NORMAL DISTRIBUTION It is a symmetrical distribution. In this, we convert x into z by the transformation: z= (x-亮)/ Total area under the normal curve is unity. P(-<z<)= 1 P(-<z<0)=P(0<z<)= 0.5 - z=0
  • 9. * Consider the following question:-