normal probability distribution function

Conclusion - In this chapter we have studied the method of evaluating probabilities of events relating to independent events and conditional events. We have also studied about random variables and their probability distributions, namely binomial distribution ..

Binomial Distribution - 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 = "pro..

>There are many daily life situations where n is very large and p is very small. In such situations, the Poisson distribution can be more conveniently used as an approximation to binomial distriburtion which may prove cumbersome for large values of n. This is called Poisson approximation ..

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. of heads ..

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, which can assume the v..

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 variable, 2. discrete ra..

Although the probability distribution of a continuous r.v cannot be presented in tabular forms, we can have a formula in the form of a function represented by f(x) usually called the probability density function..

A random experiment which has only two outcomes (success or failure) Let n independent bernoulli trials be performed and X denote the number of successes in n trials then X follows a binomial distribution. The probability of success be p, The probability of fail..

The range for the above ungrouped data is 49 - 12 = 37. Normally it is desirable to divide the range into 6 to 10 classes. Consider the class 11 - 15. If a student scores 11 marks or 15 marks, he will be put in this class. For this class, 11 is the lower limit and 15 is the upper limit an..

For the Poisson distribution, the probability function is given by Given P (x = 1) = (0.2) P (X = 2) ..