Random variables and discrete probability distributions

11 important questions on Random variables and discrete probability distributions

On what 2 variables is the normal distribution based?

1. the Mean mu, this is located exactly in the middle. If the mean moves, so does the curve
2. The standard deviation sigma. If it increases, the curve becomes flatter and wider, and vice versa

What is a stochastic variable?

Another way to say random variable.

What are the 6 steps to find the interval probability using a normal distribution?

1. Define meaning of X, what does it represent
2. Write down values mu, sigma and X
3. Draw normal distribution, and indicate mean and X value
4. Calculate Z-value using the formula: (X-mu)/sigma
5. Look up which percentage corresponds to Z-value
6. What is asked, smaller (left) or larger (right) of certain value
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When do you use an exponential distribution?

When you're interested in the probability of the occurrence of a certain time interval. e.g time between arrivals of trains

What are the symbols in an exponential distribution?

1. lambda - arrival rate
2. e - set value
3. x - value with which you want to calculate

What is the exponential distribution calculating rule?

mu = sigma = 1/lambda

What is a t-distribution?

A special kind of distribution that looks like a normal distribution but less high and spread more widely. We use t instead of x. You use it when the standard deviation of the population is unknown, so instead you use the standard deviation of the sample.

What are the symbols in a t-distribution?

1. E = expected (mean)
2. V = variance
3. df = amount of degrees of freedom

What is a chi-squared distribution (x^2-distribution)?

A positively skewed curve. The formulas for its mean and variance are:
E(x^2) = df
V(x^2) = 2 x df

How do you call a function that assigns a numerical value to each simple event in a sample space?

random variable (rv)

How do you call a table, formula, or graph that describes the values of a random variable and the probability associated with these values?

Probability distribution

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