Probability & Statistics

Problem (Poisson Distribution Examples ) Suppose that I fall sick an average of 12 times each year. Me falling sick in any time period will not affect the probability of…

Question : The lifetime in hours of an electronic tube is a random variable having a probability density function given by\[f\left(x\right)=xe^{-x} , x≥0 , 0 , otherwise\]Compute the expected lifetime…

Question : Find variance and standard deviation of the following frequency distribution. xFrequency (f)1.5202.0253.5805.0505.5257.2105.35 Solution : Sum of the frequencies \[N=\sum_{i=1}^{N}f_i=215\] (i) Arithmetic average (mean) \[\bar{x}=\frac{\sum_{i=1}^{N}{f_i\ast x_i}}{N}=\frac{30+50+280+250+137.5+72+26.5}{215}=\frac{846}{215}=3.93\] frequency distribution table…

Question : Find arithmetic average (mean) of the following data 4,3,3,3,4,4,4,4,6,4,3,3,3,3,5,5,5,3,3,3,3,4,3,4,3,3,4,4,4,4,4,3 Answer : For the given data first we shall make a frequency table xifrequency (fi) 3154135361 \[N=\sum_{i=1}^{32}(f_{i}= 15+13+3+1=32\] By…

What is P(AUBUC) formula? Question : Suppose are events in a common probability space with P(A) =0.2 , P(B) =0.2, P(C) =0.3, P(A∩B) =0.1 , P(A∩C) =0.1, P(B∩C) = 0.1…

Question : From the six letters P, Q, R, S, T and U, three letters are chosen at random with replacement. What is the probability that either the word “QPS”…

Question : What is Bernoulli Distribution ? Answer : Bernoulli Distribution : If a random variable X has only two possibilities to occur then it is called Bernoulli random variable.…

Question : Prove that the variance of cX+d is c^2 V(X)+d where X is a continuous random variable. Solution : We know that variance of a continuous random variable is…

Question : Prove that the mean of cX+d = E(X)+d where X is a continuous random variable. Solution : We know that Expectation of a continuous random variable is \[E\left(X\right)=\int_{-\infty}^{\infty}xf\left(x\right)dx\]…