Recall that for a random variable

following a Bernoulli distribution

, we have the moment-generating function (MGF)

and also recall that the MGF of a sum of i.i.d. random variables is the product of the MGFs of each distribution:

So for a sum of Bernoulli-distributed i.i.d. random variables

, we have

which is the MGF of the binomial distribution

. (Indeed, the Bernoulli distribution is identical to the binomial distribution when

.)
Answer:
K = - 6
Step-by-step explanation:
Let's solve your equation step-by-step.
2(4k+5)+3(3−3k)=25
Step 1: Simplify both sides of the equation.
2(4k+5)+3(3−3k)=25
(2)(4k)+(2)(5)+(3)(3)+(3)(−3k)=25(Distribute)
8k+10+9+−9k=25
(8k+−9k)+(10+9)=25(Combine Like Terms)
−k+19=25
−k+19=25
Step 2: Subtract 19 from both sides.
−k+19−19=25−19
−k=6
Step 3: Divide both sides by -1.
Answer: A △ABC such that the bisectors of ∠ABC and ∠ACB meet at a point O.
To prove :
∠BOC=90
o
+
2
1
∠A
Step-by-step explanation: In △BOC,
∠1+∠2+∠BOC=180
o
In △ABC,
∠A+∠B+∠C=180
o
∠A+2(∠1)+2(∠2)=180
o
2
∠A
+∠1+∠2=90
o
∠1+∠2=90
o
−
2
∠A