Questions: Question If X ~ U(4.5,18.5) is a continuous uniform random variable, what is P(X<11) ?
Select the correct answer below: 1/28 3/28 13/28 9/14 19/28
Transcript text: Question
If $X \sim U(4.5,18.5)$ is a continuous uniform random variable, what is $P(X<11)$ ?
Select the correct answer below:
$\frac{1}{28}$
$\frac{3}{28}$
$\frac{13}{28}$
$\frac{9}{14}$
$\frac{19}{28}$
FEEDBACK
MORE INSTRUCTION
SUBMIT
Content attribution
Solution
Solution Steps
Step 1: Calculate the Mean
The mean E(X) of a uniform distribution U(a,b) is given by the formula:
E(X)=2a+b
Substituting the values a=4.5 and b=18.5:
E(X)=24.5+18.5=223=11.5
Step 2: Calculate the Variance
The variance Var(X) of a uniform distribution is calculated using the formula:
Var(X)=12(b−a)2
Substituting the values:
Var(X)=12(18.5−4.5)2=12(14)2=12196=16.3333
Step 3: Calculate the Standard Deviation
The standard deviation σ(X) is the square root of the variance:
σ(X)=Var(X)=16.3333≈4.0415
Step 4: Calculate the Probability P(X<11)
The cumulative distribution function F(x;a,b) for a uniform distribution is given by: