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How do you find the expected value of X?
To find the expected value, E(X), or mean μ of a discrete random variable X, simply multiply each value of the random variable by its probability and add the products. The formula is given as E(X)=μ=∑xP(x).
How do you find the value of X with mean and standard deviation?
You take your x-value, subtract the mean , and then divide this difference by the standard deviation. This gives you the corresponding standard score (z-value or z-score). Standardizing is just like changing units (for example, from Fahrenheit to Celsius).
How to calculate the expected value of X?
Given X ∼ N ( 0, σ 2) (that is, X: R → R is a normal random variable with mean 0 and variance σ 2 ), I’m trying to calculate the expected value of X given that X > 0. I thought that integrating would do it, but the value, σ 2 π, seems to be off by a factor of 2 based on some other information I have; I think the answer should be 2 π σ.
What do you need to know about normal distributions?
A normally distributed variable X with mean μ and variance σ 2 has the same distribution as σ Z + μ where Z is a standard normal variable. All you need to know about Z is that
Which is the sampling distribution of a normal variable?
Sampling Distribution of a Normal Variable . Given a random variable . Suppose that the X population distribution of is known to be normal, with mean X µ and variance σ 2, that is, X ~ N (µ, σ). Then, for any sample size n, it follows that the sampling distribution of X is normal, with mean µ and variance σ 2 n, that is, X ~ N µ, σ n .
How to find the normal probabilities of a variable?
Appendix E, Table I (Or see Hays, p. 924) reports the cumulative normal probabilities for normally distributed variables in standardized form (i.e. Z-scores). That is, this table reports P(Z ≤ z) = F(z). For a given value of Z, the table reports what proportion of the distribution lies below that value.