The joint probability mass function of x and y is given by p(1,1)=0.4 p(2,1)=0.05, p(3,1)=0.1, p(1,2)=0.05, p(2,2)=0, p(3,2)=0.05, p(1,3)=0.1, p(2,3)=0.05, p(3,3)=0.2 (a) compute the conditional mass function of y given x=2: p(y=1|x=2)= 0.5 p(y=2|x=2)= 0 p(y=3|x=2)= 0.5 (b) are x and y independent? i. yesii. no (c) compute the following probabilities: i. p(x+y> 4)= ii. p(xy=3)= iii. p(xy> 2)=

answer:

step-by-step explanation:

here, the total dishes = 10

dishes having meat = 3 ( chicken, meatloaf and hamburger )

thus, the probability of having meat on the chosen dishes = number of dishes having meat / total dishes

=

therefore, the probability of not having meat = 1- the probability of having meat on the chosen dishes

=

=

=

⇒ option b is correct.

step-by-step explanation:

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.