Question

jordan wants to play a basketball game at a carnival. the game costs the player $5 to play, and the player gets to take two long - distance shots. if they miss both shots, they get nothing. if they make one shot, they get their $5 back. if they make both shots, they get $10 back. jordan has a 40% chance of making this type of shot.
here is the probability distribution of ( x ) = the number of shots jordan makes in a randomly selected game, and ( m ) = the amount of money jordan gains from playing the game.

( x=# ) of shots made

0

1

2

---

---

---

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( m = ) money gained

( -$ 5 )

( $ 0 )

( $ 5 )

probability

0.36

0.48

0.16

calculate the mean of ( x ).
( mu_{x}=) shots made

Explanation:

Step1: Recall the formula for the mean of a discrete random variable

The formula for the mean \(\mu_X\) of a discrete random variable \(X\) is \(\mu_X=\sum_{i}x_ip_i\), where \(x_i\) are the possible values of \(X\) and \(p_i\) are their corresponding probabilities.

Step2: Substitute the values into the formula

Here, \(x_1 = 0\), \(p_1=0.36\); \(x_2 = 1\), \(p_2 = 0.48\); \(x_3=2\), \(p_3=0.16\).

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Step3: Calculate the sum

\(0.48 + 0.32=0.8\)

Answer:

\(0.8\)