Gauss M.D. said:Homework Statement
We have two normally distributed random variables:
A = N(129, 29.4)
B = N(86, 24.0)
What is the probability A is atleast twice the size of B?
The Attempt at a Solution
P(A > 2B | B = b) or something? I think we are supposed to use the CLT somehow but I don't know how when it's conditional...
A conditional normal distribution is a type of probability distribution in which the values of a random variable are dependent on the values of one or more other variables. In other words, the probability of an outcome is influenced by certain conditions or factors.
A regular normal distribution has a fixed mean and standard deviation, while a conditional normal distribution has a variable mean and standard deviation depending on the conditions or factors that are present. This means that the shape of a conditional normal distribution can change depending on the values of the variables it is conditioned on.
The formula for calculating the conditional normal distribution is:
P(x | y) = (1/σ√2π) * e^-(x-μ)^2 / (2σ^2)
Where x is the random variable, y is the conditioning variable, σ is the standard deviation, and μ is the mean.
The conditional normal distribution is commonly used in various fields such as finance, economics, and engineering to model relationships between variables. For example, it can be used to analyze stock market data, predict economic trends, and study the effects of different factors on a system.
The conditional normal distribution is closely related to regression analysis, which is a statistical technique used to model the relationship between a dependent variable and one or more independent variables. In regression analysis, the conditional normal distribution is used to represent the random errors or residuals in the model, which are assumed to follow a normal distribution.