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Sagot :
The correct answer is : c) As the number of experiments increases, the mean of the observations will approach the mean of the random variable.
Mean of random Variable x :
The expected value of a discrete random variable X, symbolized as E(X), is often called the long-term average or mean (symbolized as μ). This means that if you run the experiment many times over time, you would expect this average. For example, let X = the number of heads you get when you toss 3 fair coins. If we repeat this experiment (tossing 3 fair coins) many times, the expected value of X will be the expected average number of heads per 3 tosses.
Standard Deviation of Random Variable:
A measure of the variance of a random variable distribution that determines how for a value is from its expected value.
The standard deviation of a random variable X is often written as σ or σₓ.
For discrete random variables, the standard deviation is computed by taking the square of the difference between the value of the random variable and the expected value multiplied by the associated probability of the value of the random variable. Calculate the value of a random variable and finally take the square root.
In symbols σ = √ (x - μ)² P(X =x)
The equivalent formula is σ = [tex]\sqrt{E(x^{2}) - [{E(x^2)]}[/tex]
The square of the standard deviation equals the variance Var(X) = σ².
Learn more about Random Variable:
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