Consider a single tossing of x unbiased coins: a) Find the probability pX(x) of obtaining all heads; [2]

b) If x is regarded as a continuous variable in the range 0 ≤ x < ∞, show

that pX(x), regarded as a function of x and suitably scaled, determines

a probability distribution; [5]

c) Obtain a pdf of this distribution and calculate its cumulant generating

function; [5]

d) Hence or otherwise, show that the mean and variance are 1

ln 2 and

1

(ln 2)2 , respectively. [8]

e) Verify that the coefficient skewness for this distribution is γ3 = 2. [5]

1/3

step-by-step explanation:

to find this, you can divide 12 by 4 which is 3 or you can multiply 4 until you reach 12 (4x3=12). both should give you 3, meaning theres three times less bananas than there are oranges.

the area of a triangle is determined by the formula: base x height * 1/2

you'll need to assign a base to the triangle. based on the vertices given, the simplest base would be the line segment from (-2,1) to (2,1). the distance between any two numbers is found by just subtracting them. here, you should subtract the x values to find the distance of this side.

2 - (-2) = 4.

so the distance (aka the length of the base) is 4. the height of the triangle is the distance between the base and the highest point on the triangle which is (3,4). we should subtract the y values this time to find the height/distance.

4 - 1 = 3

so the height is 3.

base = 4

height = 3

hope this if needed hmu

we know that

1) the inscribed angle measures half of the arc it comprises.

so

m∠dgf= > expression

2) the opposite angles in an inscribed quadrilateral are supplementary angles

so

m∠dgf=

m∠dgf=°

substitute in the expression to find the value of arc ef

therefore

the answer is

the measure of the arc ef is