Probability

PROBABILITY CLASS 12

by Indu Khurana

Probability of binomial distribution

​

​

​Where P is the probability of success and q is the probability of failure

​n and p are called parameters of binomial distribution

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​ =

Mean of binomial distribution= nxp

Variance of binomial distribution= npq

Standard deviation of binomial distribution= √npq

​Poisson Distribution

​Probability P(r)= ,

​

​Recurrence formula: P(r+1)=

​

​Mean and variance=

Standard deviation =

​Normal distribution

Multiple Choice

If X is a normal distribution random variable with  $$\mu=10$$   and  $$\sigma=2$$  , find P(X  $$<9.8$$  )

• 0.4602

• 0.4206

• 0.4620

• 0.4260

Multiple Choice

If X is a normal distribution random variable with  $$\mu=10$$   and  $$\sigma=2$$  , find

P( $$12<$$  X  $$<14.5$$  )

• 0.1546

• 0.1456

• 0.1465

• 0.1645

Multiple Choice

If Z is a standard normal variable, find  $$P\left(-2.38<Z<-1.45\right)$$  

• $$F\left(1.45\right)-F\left(-2.38\right)$$  

• $$F\left(-1.45\right)-F\left(-2.38\right)$$  

• $$F\left(-1.45\right)-F\left(2.38\right)$$  

• $$F\left(-2.38\right)-F\left(-1.45\right)$$  

Multiple Choice

The standard deviation of a poisson variate X is √3. Find the probability X=2, given  $$e^{-3}=0.0498$$  

• 0.2142

• 0.2421

• 0.2214

• 0.2241

Fill in the Blanks

Mean of poisson distribution is 6.25. Find its standard deviation.

Fill in the Blanks

Find the probability that 5 defective fuses will be found in a box of 200 fuses if 2% of fuses are defective. Given $e^{-4}=0.018$  

Fill in the Blanks

A die is thrown three times. Find the mean and variance of probability distribution of number of sixes

Fill in the Blanks

In a binomial distribution, the sum of its mean and variance is 1.8. Find the probability of two successes if the event was conducted 5 times.

Multiple Choice

A die is tosses 3 times. Getting an even number is success. Find the binomial distribution and its variance.

• $$\left(\frac{1}{2}+\frac{1}{2}\right)^3,\ \frac{1}{4}$$  

• $$\left(\frac{1}{2}+\frac{1}{2}\right)^3,\ \frac{3}{4}$$  

• $$\left(\frac{1}{2}+\frac{1}{2}\right)^3,\ \frac{2}{4}$$  

• $$\left(\frac{1}{2}+\frac{1}{2}\right)^3,\ \frac{3}{2}$$  

Fill in the Blanks

Die is thrown 3 times. Getting 2 is a success. Find its expectation.