Probability Distributions and Their Properties

This video tutorial covers various probability distributions, including binomial, geometric, Poisson, uniform, and exponential distributions. It explains the formulas for calculating probabilities, means, variances, and standard deviations for each distribution. The video also provides insights into how these distributions are used in probability theory and offers a formula sheet for reference.

What is the formula for the probability of getting X successes in a binomial distribution?

• nCx * p^X * q^(n-X)

• nPx * p^X * q^(n-X)

• nCx * q^X * p^(n-X)

• nPx * q^X * p^(n-X)

In a geometric distribution, what is the probability that the nth event will be successful?

• P^n * Q

• Q^n * P

• P^(n-1) * Q

• Q^(n-1) * P

What is the mean of a geometric distribution?

• 1/P

• P

• 1-Q

• Q

For a Poisson distribution, what is the relationship between the mean and lambda?

• Mean is equal to lambda

• Mean is twice lambda

• Mean is the square of lambda

• Mean is half of lambda

In a Poisson distribution, how do you calculate the probability that X is greater than n?

• e^(lambda) * sum(X=0 to n) (lambda^X / X!)

• 1 - e^(lambda) * sum(X=0 to n) (lambda^X / X!)

• 1 - e^(-lambda) * sum(X=0 to n) (lambda^X / X!)

• e^(-lambda) * sum(X=0 to n) (lambda^X / X!)

What is the formula for the probability density function of a uniform distribution?

• (b-a)/2

• 1/(b-a)

• b/(a-b)

• a/(b-a)

How do you calculate the mean of a uniform distribution?

• a*b

• a+b

• (a-b)/2

• (a+b)/2

In an exponential distribution, what is the relationship between the mean and lambda?

• Mean is 2*lambda

• Mean is lambda^2

• Mean is 1/lambda

• Mean is lambda

What is the formula for the probability density function of an exponential distribution?

• lambda * x * e^(-x)

• lambda * e^(-lambda * x)

• x * e^(-lambda)

• e^(-lambda * x)

How do you calculate the variance of an exponential distribution?

• 1/lambda^2

• lambda^2

• 1/lambda

• lambda