You and a friend play a game where you each toss a balanced coin. if the upper faces on the coins are both tails, you win $1; if the faces are both heads, you win $6; if the coins do not match (one shows a head, the other a tail), you lose $3 (win (−$ calculate the mean and variance of y, your winnings on a single play of the game. note that e(y) > 0.

 The mean and variance of Y is $0.25 and $6.19 respectively.

Step-by-step explanation:

Given : You and a friend play a game where you each toss a balanced coin.

sample space for tossing two coins : {TT, HT, TH, HH}

Let Y denotes the  winnings on a single play of the game.

You win $1; if the faces are both heads

then P(Y=1)=P(TT)=

You win $6; if the faces are both heads

then P(Y=6)=P(HH)=

You loose $3; if the faces do not match.

then P(Y=1)=P(TH, HT)=

The expected value to win : E(Y)=

Hence, the mean of Y : E(Y)= $0.25

Variance =

Hence, variance of Y = $ 6.19

answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.

answer: -10

step-by-step explanation:

s(t) = 1 - 10t

s(x) = 1 - 10x

s(x + h) = 1 - 10(x + h)

            = 1 - 10x - 10h

s(x + h) - s(x) = 1 - 10x - 10h - (1 - 10x)

                      = 1 - 10x - 10h - 1 + 10x

                      = -10h

= -10