Cconsider a game in which players roll a number cube to determine the number of points earned. if a player rolls a prime number, that many points will be added to the player’s total. any other roll will be deducted from the player’s total. what is the expected value of the points earned on a single roll in this game?

E(X) = 1/6

Step-by-step explanation:

Given:-

- A numbered cube is rolled.

+ Points : Prime Number

- Points : Any other number.

Find:-

What is the expected value of the points earned on a single roll in this game?

Solution:-

- We will denote a random variable (X) that represents the number of points in a game. We have 6 faces with (1 , 2 , 3 , 5) as prime numbers ( + Points ). Where numbers ( 4 & 6 ) will denote the ( - Points ).

- We will express the random variable (X) in probability distribution table. The probability of getting any number on the cube is equal to (1/6). The distribution table is as follows:

          X        -6           -4             1            2           3            5

      P(X)        1/6         1/6           1/6         1/6        1/6          1/6

- The expected value for the random variable E(X) can be determined by the following formula:

                    E(X) = Sum ( Xi*P(X) )

Where,   i : Term number from table:

                    E(X) = (-6)*(1/6) + (-4)*(1/6) + (1)*(1/6) + (2)*(1/6) + (3)*(1/6) + (5)*(1/6)

                    E(X) = (1/6)* ( -6 -4 + 1 + 2 + 3 + 5 )

                    E(X) = ( 1 / 6 ) * ( 1 )

                    E(X) = 1/6

- The expected value of points earned per single roll in this game is 1/6

plants store their excess carbohydrate in the form of starch so that it could be used as energy source later on. the excess carbohydrate is converted into starch in the plastid i.e. chloroplast & this process occurs in the presence of sunlight. it is an insoluble polymer of glucose which gets stored in cell organelles named as amyloplasts. in some plants, starch is also stored in roots and embryos.