Histogram g If a fair coin is tossed 4 times, there are 16 possible sequences of heads (H) and tails (T). Suppose The random variable X represents the number of heads in a sequence. Construct the probability distribution for X.

P(X = 0) =

P(X = 1) =

P(X = 2) =

P(X = 3) =

P(X = 4) =

Step-by-step explanation:

The sample space for a coin tossed 4 types is given below:

The Probability distribution for the number of heads, X is given as:

P(X = 0) =

P(X = 1) =

P(X = 2) =

P(X = 3) =

P(X = 4) =

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: