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This Question: 1 pt 12 of 44 (0 complete) This Quiz: 44 pts possible Verify Property 2 of the definition of a probability density function over the given interval. ffx) 22x What is Property 2 of the definition of a probability density function? O A. The area under the graph of f over the interval [a,bl is b O B. The area under the graph of f over the interval [a.b] is 1 O C. The area under the graph of f over the interval [a,b is a. Since the given interval. [0.oo), has a right-endpoint of infinity, the area under the graph of fwill be calculated using an improper integral. Choose the correct formula for an improper integral over the interval [a,ool below t(x) dx= lim | f(x) dx= lim [F(x)]a= lim (F(b)-F(a)) b-o0 f(x) dx = lim | f(x) dx = lim [F(x)]-lim (F(a)-F(b)) b- 00 b--0o f(x) dk- lim x) dx- lim [F(x)m (F(b)-F(a)) b-+00 O D. 00 f(x) dx= lim f(x) dx= lim [F(棴= lim (F(a)-F(b)) b--oã Substitute a and b into the left side of the formula from the previous step and express the integral as a limit. area 2edx lim2edx Next, determine F(x). First, find the antiderivative of f. 2(Use C as the artbitrary constant.) Next, determine F(x). First, find the antiderivative of f. as the anbliay cosat) Let C 0 in the expression obtained above and let the resulting expression be F(x). Evaluate the result over [0,oo) using the far right side of the formula for the area. area = As b approaches oo, e approaches infinity where c is a constant. Use this fact to calculate the limits from the previous step area+1 Is Property 2 of the definition of a probability density function over the given interval now verified? Choose the correct answer below A Property 2 o the definition o a probability density unction over the given interval has been ver ed since the expression in the previous step simplifies to o B. Property 2 of the definition of a probability density function over the given interval has not been verified because the expression in the previous step does not simplify to the expected area value. ° C. â D Property 2 ofthe definition of a probability density function over the given interval has been verified since the expression in the previous step simplifies to 0 Property 2 o the definition o a probability density unction over the given interval has been ve ned since the expressio n e evious ste si plifies to 1. Show transcribed image text
This Question: 1 pt 12 of 44 (0 complete) This Quiz: 44 pts possible Verify Property 2 of the definition of a probability density function over the given interval. ffx) 22x What is Property 2 of the definition of a probability density function? O A. The area under the graph of f over the interval [a,bl is b O B. The area under the graph of f over the interval [a.b] is 1 O C. The area under the graph of f over the interval [a,b is a. Since the given interval. [0.oo), has a right-endpoint of infinity, the area under the graph of fwill be calculated using an improper integral. Choose the correct formula for an improper integral over the interval [a,ool below t(x) dx= lim | f(x) dx= lim [F(x)]a= lim (F(b)-F(a)) b-o0 f(x) dx = lim | f(x) dx = lim [F(x)]-lim (F(a)-F(b)) b- 00 b--0o f(x) dk- lim x) dx- lim [F(x)m (F(b)-F(a)) b-+00
O D. 00 f(x) dx= lim f(x) dx= lim [F(棴= lim (F(a)-F(b)) b--oã Substitute a and b into the left side of the formula from the previous step and express the integral as a limit. area 2edx lim2edx Next, determine F(x). First, find the antiderivative of f. 2(Use C as the artbitrary constant.)
Next, determine F(x). First, find the antiderivative of f. as the anbliay cosat) Let C 0 in the expression obtained above and let the resulting expression be F(x). Evaluate the result over [0,oo) using the far right side of the formula for the area. area = As b approaches oo, e approaches infinity where c is a constant. Use this fact to calculate the limits from the previous step area+1 Is Property 2 of the definition of a probability density function over the given interval now verified? Choose the correct answer below A Property 2 o the definition o a probability density unction over the given interval has been ver ed since the expression in the previous step simplifies to o B. Property 2 of the definition of a probability density function over the given interval has not been verified because the expression in the previous step does not simplify to the expected area value. ° C. â D Property 2 ofthe definition of a probability density function over the given interval has been verified since the expression in the previous step simplifies to 0 Property 2 o the definition o a probability density unction over the given interval has been ve ned since the expressio n e evious ste si plifies to 1.
Show transcribed image text Jarrod RobelLv2
7 Oct 2019