discrete/continuous random variables

random variable is a function which associates a real number to each outcome of a random experiment..

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. ..

A random variable which can assume all possible values between certain limits is called a continuous random variable..

random variables which can assume any value over an interval..

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...

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 variabl..

Let X be continuous random variable which can assume values in the interval [a,b]. A function f(x) on [a,b] is called the probability density function if ..

Let X be a discrete random variable which can assume values x 1 , x 2 , x 3 ,x n with probabilities p 1 , p 2 , p 3 .. p n respectively then (a) Mean of X or expectation of X denoted by E(X) or m is given by (b) Variance of X denoted by s 2 is given ..

In a random sample of 25 trees, the variance in height was found to be 6.9. Find the 95% confidence interval for the standard deviation. Assume that the variable is normally distributed. => between 4.9 and 13.7 or between 4.2 and 13.4 or between 5.5 and 14.1 or between 5.5 and 1..

The average age of employees in a firm is 35 years. Assume the variable is normally distributed. If the standard deviation is 3 years, then find the probability that the age of a randomly selected employee will be greater than 38 years. => 15.87% or 65.87% or 34.13% or 94.13%..