Respuesta :
The value of E(X) is [tex]\frac{9}{4}[/tex].
What is an indicator random variable?
A variable with a value of 1 if event A occurs and a value of 0 otherwise is the indicator variable. With the exception of the fact that its argument is random as defined by the probability space, the indicator random variable is virtually identical to the indicator function.
Let [tex]X_{j}[/tex] be the indicator random variable of HH appearing at position j for j = 1,2,......,9. Notice that these aren't quite independent from each other, so if the binomial solution is entirely accurate, it gives the correct expected value.
But we can anyway use linearity of the expectation. As [tex]$X=\sum_{j=1}^9 X_j$[/tex], in another word, X, which is the total number of appearances of HH, is the sum of the ones that did occur, we get that
[tex]$\mathbb{E}[X] = \mathbb{E} \left[\sum_{j=1}^9 X_j \right] \\=\sum_{j=1}^9 \mathbb{E}[X_j] \\= \sum_{j=1}^9 \frac{1}{4} \\= \frac{9}{4}.$[/tex]
Therefore, the value of E(X) is [tex]\frac{9}{4}[/tex] .
To know more about indicated probability, visit: https://brainly.com/question/17330584
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