# Recent questions and answers in Probability Distribution

### If $X$ a normal variate with mean $80$ and standard deviation $10$ compute the following probabilites by standardizing. $P(70$$<X) ### If X a normal variate with mean 80 and standard deviation 10 compute the following probabilities by standardizing. P(65\leqX\leq100) ### If X a normal variate with mean 80 and standard deviation 10 compute the following probabilities by standardizing.P(X\leq80) ### If X a normal variate with mean 80 and standard deviation 10 compute the following probabilities by standardizing. P(X\leq100) ### 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]. ### 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]. ### 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]. ### 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]. ### 20\% of the bolts produced in a factory are found to be defective. Find the probability that in a sample of 10 bolts chosen at random exactly 2 will be defective using ,Poisson distribution. [e^{-2}=0.1353]. ### 20\% of the bolts produced in a factory are found to be defective. Find the probability that in a sample of 10 bolts chosen at random exactly 2 will be defective using ,Binomial distribution. ### 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]. ### 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 ### Let x have a poisson distribution with mean 4.FindP(2\leqX<5)[e^{-4}=0.0183]. ### Let X have a poisson distribution with mean 4.Find (i) \;P(X\leq 3)\qquad[e^{-4} = 0.0183]. ### In a hurdle race a player has to cross 10 hurdles. The probability that he will clear each hurdle is \large\frac{5}{6}. What is the probability that he will knock down less than 2 hurdles. ### The overall percentage of passes in a certain examination is 80.If 6 candidates appear in the examination what is the probability that atleast 5 pass the examination. ### Four coins are tossed simultaneously .what is the probability of getting at most two heads ### Four coins are tossed simultaneously.what is the probability of getting at least two heads ### Four coins are tossed simultaneously .what is the probability of getting exactly 2 heads ### If on an average 1 ship out of 10 do not arrive safely to ports. Find the mean and the standard deviation of ship returning safely out of a total of 500 ships ### A die is thrown 120 times and getting 1 or 5 is considered a success.Find the mean and variance of the number of successes. ### The mean of a binomial distribution is 6 and its standard deviation is 3. Is this statement true or false?comment? ### Find the mean and variance for the following probability density functions f(x) = \left\{ \begin{array}{l l} xe^{-x}, & \quad \text{if x$$>$0}\\ 0, & \quad \text{otherwise} \end{array} \right.$### Find the mean and variance for the following probability density functions$f(x) = \left\{ \begin{array}{l l} \alpha e^{-\alpha x} ,& \quad \text{if $x$$>$$0$}\\ 0 ,& \quad \text{otherwise} \end{array} \right.$### Find the mean and variance for the following probability density functions$f(x) = \left\{ \begin{array}{l l} \frac {1}{24} ,& \quad \text{-12$\leq$$x$$\leq $$12}\\ 0, & \quad \text{otherwise} \end{array} \right. ### The probability distribution of a random variable x is given below:  \begin{array} {llllllll} \textbf{X:}& 0& 1& 2& 3 \\ \textbf{P(X=x):}& 0.1& 0.3 &0.5& 0.1& \end{array} If Y=X^{2}+2X find the mean and variance of Y. ### In a gambling game a man wins Rs.10 if he gets all heads or all tails and loses Rs.5 if he gets 1 or 2 heads when 3 coins are tossed once. Find his expectation of gain. ### Two cards are drawn with replacement from a well shuffled deck of 52 cards. Find the mean and variance for the number of aces. ### In an entrance examination a student has to answer all the 120 questions. Each question has four options and only one option is correct. A student gets 1 mark for a correct answer and loses half mark for a wrong answer. What is the expectation of the mark scored by a student if he chooses the answer to each question at random? ### Find the expected value of the number on a die when thrown. ### A die is tossed twice. A success is getting as odd number on a toss. Find the mean and the variance of the probability distribution of the number of successes. ### A random variable x has a probability density function f(x) = \left\{ \begin{array}{l l} k & \quad \text{0<x<2n}\\ 0 & \quad \text{elsewhere} \end{array} \right. Find p(\large\frac{\pi}{2}<x<\frac{3\pi}{2}) ### A random variable x has a probability density function f(x) = \left\{ \begin{array}{l l} k & \quad \text{0<x<2n}\\ 0 & \quad \text{elsewhere} \end{array} \right. Find p(0<x<\large\frac{\pi}{2}) ### A random variable x has a probability density function f(x) = \left\{ \begin{array}{1 1} k & \quad 0 < x < 2n \\ 0 & \quad \text{else where} \end{array} \right. Find k ### A continuous random variable x has the p.d.f defined by f(x) = \left\{ \begin{array}{1 1} ce^{-ax} & \quad 0 < x < \infty \\ 0 & \quad \text{else where} \end{array} \right. Find the value of c if a>0 ### For the distribution function given by f(x) = \left\{ \begin{array}{l l} 0&\quad\text{x<0}\\ x^{2} & \quad \text{0$$\leq$$x$$\leq$$1}\\ 1 & \quad \text{x>1} \end{array} \right. Find the density function. Also evaluate p(x>0.75) ### For the distribution function given by f(x) = \left\{ \begin{array}{l l} 0&\quad\text{x<0}\\ x^{2} & \quad \text{0$$\leq$$x$$\leq$$1}\\ 1 & \quad \text{x>1} \end{array} \right. Find the density function. Also evaluate p(x\leq0.5) ### For the distribution function given by f(x) = \left\{ \begin{array}{l l} 0&\quad\text{x<0}\\ x^{2} & \quad \text{0$$\leq$$x$$\leq$$1}\\ 1 & \quad \text{x>1} \end{array} \right. Find the density function. Also evaluate p(0.5< x <0.75) ### The probability density function of a random variable x is f(x) = \left\{ \begin{array}{l l} kx^{\alpha-1}e^{-\beta\;x^{\alpha}}, & \quad \text{x,\alpha$$,\beta$>$0$}\\ 0 ,& \quad \text{elsewhere} \end{array} \right.$, Find$p(x$>$10)\$

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