Answer:

Step-by-step explanation:
Given Equation:

Solving the bracket on L.H.S

Taking the terms of 'x' to one side and the constants to other side

The value of 'x' after solving the equation is:

Answer:

Step-by-step explanation:

C can be found using pythagoras theorem. c2=a2+b2. Now, b is not given, but we know that cos(theta)=b/c=>b=c*cos(theta). Substituting b in the above relation, c2=a2+c2(cos(theta))^2=>c2=a2/(1-cos((theta))^2). c is the squareroot of c2. Hence c=sqrt(2/(1-cos((theta))^2))
Answer:
a.
.
b. 
Step-by-step explanation:
By the definition, the expected value of a random variable X with probability mass function p is given by
where the sum runs over all the posible values of X. Given a function g, the random variable Y=g(X) is defined. Note that the function g induces a probability mass function P' given by P'(Y=k) = P(X=g^{-1}(k)) when the function g is bijective.
a. Note that for 1/3ln(2)+1/6ln(5) by choosing the function g(x) = ln(x) the expression coincides with E(g(x)), because if Y = g(x) then E(Y) = P'(Y=1)*ln(1)+P'(Y=2)*ln(2)+P'(Y=5)*ln(5) = P(X=1)*ln(1)+P(X=2)*ln(2)+P(X=5)*ln(5).
b. On the same fashion, the function g(x) = xe^{xt} fullfills the expression of E[g(X)]