Question

Consider the following exponential probability density function.  for x ≥ 0 If needed, round your answer to four decimal digits.(a) Find P(x ≤ 2). (b) Find P(x ≥ 3). (c) Find P(x ≤ 5). (d) Find P(2 ≤ x ≤ 5).

Answer 1

Answer:

Here the general formula is

$P(X\leq x_{0} )=1 - e^{\frac{-x_{0}}{2} }$

a) $P(X\leq 2 )= 0.6321$

b) $P(X\geq 3 )= 0.2231$

c) $P(X\leq 5 )= 0.9179$

d) $P(2\leq X\leq 5 )= 0.2858$

Step-by-step explanation:

Now the solutions are,

a)

$P(X\leq 2 )=1 - e^{\frac{-2}{2} }\\P(X\leq 2 )= 0.6321$

b)

$P(X\geq 3 )=1-[1 - e^{\frac{-3}{2} }]\\P(X\geq 3 )= 0.2231$

c)

$P(X\leq 5 )=1 - e^{\frac{-5}{2} }\\P(X\leq 5 )= 0.9179$

d)

$P(2\leq X\leq 5 )=1 - e^{\frac{-5}{2} }-1 - e^{\frac{-2}{2} }\\P(2\leq X\leq 5 )= 0.2858$