Question

three coins are tossed simultaneously, x is the number of heads. find expected value and variance of x.​

Answer 1

Answer:

0.75

Step-by-step explanation:

p=1/2  

q=1-1/2

n=3

E(x)=3*1/2=1.5

Var(x)=3*1/2*1/2

Var(x)=0.75

Answer 2

Let X be the number of heads obtained when three coins are tossed simultaneously. Then X can take values 0, 1, 2 or 3.

The probability distribution of X is given by:

P(X = 0) = P(TTT) = 1/8 P(X = 1) = P(HTT, THT, TTH) = 3/8 P(X = 2) = P(HHT, HTH, THH) = 3/8 P(X = 3) = P(HHH) = 1/8

The expected value of X is given by:

E(X) = ΣxP(X=x) = (0x1/8) + (1x3/8) + (2x3/8) + (3x1/8) = 1.5

The variance of X is given by:

Var(X) = E(X2)-[E(X)]2 = Σx2P(X=x)-[E(X)]2 = (021/8)+(123/8)+(223/8)+(321/8)-[1.5]^2 = 0.75

Expected value and variance are two important concepts in probability theory. Expected value is a measure of central tendency that represents the long-run average value of a random variable if we repeat an experiment many times. Variance measures how much the values are spread out around their mean.

In this problem, we know that X can take four possible values (0, 1, 2 or 3), and we know their probabilities based on how many heads we get when three coins are tossed simultaneously. We use these probabilities to calculate the expected value and variance of X.

To learn more about probability from the given link.

https://brainly.in/question/996463

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