random distributions

Random Variable and Probability Distribution - If is often very important to allocate a numerical value to an outcome of a random experiment. For example consider an experiment of tossing a coin twice and note the number of heads (x) obtained. Outcome : HH HT TH TT No...

Let S be a sample space associated with a given random experiment. A real valued function X which assigns to each w i S, a unique real number, X( w i ) = x i is called a random variable . Two types of random variables are 1. Continuous random..

If is often very important to allocate a numerical value to an outcome of a random experiment. For example consider an experiment of tossing a coin twice and note the number of heads (x) obtained. Outcome : HH HT TH TT No. of heads (x) : 2 1 1 0 x is called a random variable, wh..

There are 5 defective items in a batch of 25 items. 4 are chosen at random. Find the probability distribution of the defective items. => II or IV or I or III..

. While one container is filled with a liter of helium gas, the other is filled with a liter of neon gas. The two gases are non-reacting (being inert gases). When the valve is opened, it is observed that the two gases get mixed together spontaneously. During the mixing, there is a negligible energy..

The average price of a computer is $750. If prices of computers are approximately normally distributed with a standard deviation of $75, then what is the probability that a randomly selected computer costs more than $1000? => 3.3% or 0.33% or 0.04% or 0.4%..

The cumulative frequency for the distribution of the distance (in miles) that 20 randomly selected runners ran during a week is given in the ogive. Find the interquartile range for the data by constructing a box plot. => 18.5, Figure 2 or 11.2, Figure 2 or 23.5, Figure 1 or 12, ..

If x is a discrete random variable assuming the values x 1 , x 2 , x 3 ,….,x n with probabilities p 1 , p 2 , p 3 ,…., p n respectively then (x 1 ,p 1 ), (x 2 , p 2 ),…(x n , p n ) defines a probability distribution of X. Mathematical Expectation of X ..

A trial, which has only two outcomes i.e., "a success" or "a failure", is called a Bernoulli trial. Let X be the number of successes in a Bernoulli trial, then X can take 0 or 1 and P(X =1) = p = "probability of a success" P(X = 0) = 1 - p = q = "probability of failure". Consider a random..

where l is a finite number and is equal to np. The sum of the probabilities P(X = r) or simply P(r) for r = 0, 1, 2, is 1. This can be seen by putting r = 0, 1, 2, in (4) and adding all the probabilities. Also, each of the probabilities is a non-negative fraction. This leads to the distributio..