4. Suppose a particular state allows individuals filing tax returns to itemize deductions only if the total of all itemized deductions is at least $5000. Let X (in 1000s of dollars) be the total of itemized deductions on a randomly chosen form. Assume that X has the pdf f(x; a) 5 5 kyxa x $ 5 0 otherwise a. Find the value of k. What restriction on a is necessary? b. What is the cdf of X? c. What is the expected total deduction on a randomly chosen form? What restriction on a is necessary for E(X) to be finite? d. Show that ln(X/5) has an exponential distribution with parameter a 2 1.

step-by-step explanation:

answer: the prove is mentioned below.

step-by-step explanation:

an isometric rigid transformation is a transformation of the plane that preserves lengths and angles.    

that is, the pre-image and the image under a rigid transformation will be congruent.

here, given: cb ║ ed and cb ≅ ed

prove that: δ cbf ≅ δ edf

since, cb ║ ed

therefore, by the alternative interior angle theorem,

∠fcb ≅ ∠fed

∠fbc ≅ ∠ fde

and, cb ≅ ed ( given)

therefore, the angles and sides are persevered after transformation.

thus, by the definition of isometric rigid transformation,

δ cbf ≅ δ edf