Question

Mean and Variance of:

continuous uniform distribution,

normal distribution,

normal approximation for binomial and Poisson distributions,

exponential distribution.

and Continuous random variables Cumulative Distribution Function.

In your own words summarize the above in three to five long sentences

Answer 1

Mean and Variance of continuous uniform distribution:

The mean is the average of all the values in the distribution. The standard deviation is the square root of the average of the squared deviations of all values from the mean. The square of standard deviation is the variance.

To find Mean of a continuous uniform distribution: The mean of X is μ=a+b2 μ = a + b 2 . X is continuous. The probability P(c < X < d) may be found by computing the area under f(x), between c and d.

To find Variance of a continuous uniform distribution:For a random variable following this distribution, the expected value is then m₁ = (a + b)/2 and the variance is m₂ − m₁² = (b − a)²/12.

Mean and Variance of normal distribution:

[ m , v ] = normstat( mu , sigma ) returns the mean and variance of the normal distribution with mean mu and standard deviation sigma . The mean of the normal distribution with parameters µ and σ is µ, and the variance is σ².

Mean and Variance ofnormal approximation for binomial and Poisson distributions:

The binomial and Poisson distributions are discrete random variables, whereas the normal distribution is continuous. You need to take this into account when we are using the normal distribution to approximate a binomial or Poisson using a continuity correction.When the value of n in a binomial distribution is large and the value of p is very small, the binomial distribution can be approximated by a Poisson distribution. If n > 20 and np < 5 OR nq < 5 then the Poisson is a good approximation.

Mean and Variance of exponential distribution:

In probability theory and statistics, the exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate.Let X be a continuous random variable with the exponential distribution with parameter β. Then the variance of X is: var(X)=β2

Mean and Variance of Continuous random variables Cumulative Distribution Function:

Let X be a continuous random variable with mean µ. The variance of X is Var(X) = E((X − µ)2). These are exactly the same as in the discrete case.If X is a continuous random variable with p.d.f. f(x) defined on a ≤ x ≤ b, then the cumulative distribution function (c.d.f.), written F(t) is given by: So the c.d.f. is found by integrating the p.d.f. between the minimum value of X and t.