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Question1 [8 marks] Suppose that the error in the reaction temperature, in $^\circ$C, for a controlled laboratory is continuous random variable X having the probability density function is given by $f(x) = \begin{cases} Kx^2 & -1 < X < 2 \\ 0 & \text{elsewhere} \end{cases}$ a) Find the value of K. [3 marks] b) Find the distribution function of x [3marks] c) Find P(0 < X < 1) [2marks]

          Question1 [8 marks]
Suppose that the error in the reaction temperature, in $^\circ$C, for a controlled laboratory is continuous
random variable X having the probability density function is given by
$f(x) = \begin{cases} Kx^2 & -1 < X < 2 \\ 0 & \text{elsewhere} \end{cases}$
a) Find the value of K. [3 marks]
b) Find the distribution function of x [3marks]
c) Find P(0 < X < 1) [2marks]

Question1 [8 marks]
Suppose that the error in the reaction temperature, in ^∘C, for a controlled laboratory is continuous
random variable X having the probability density function is given by
f(x) = Kx^2 -1 < X < 2
0 elsewhere
a) Find the value of K. [3 marks]
b) Find the distribution function of x [3marks]
c) Find P(0 < X < 1) [2marks]

Added by Javier W.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Thuc Nguyen

Step 1

In other words, we need to find the value of K that satisfies the equation: ∫f(x)dx = 1 Since f(x) is defined as 0 for x < -1 and x > 2, we only need to consider the interval -1 ≤ x ≤ 2. In this interval, f(x) is constant and equal to K. Show more…

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Suppose that the error in the reaction temperature, in Â°C, for a controlled laboratory is a continuous random variable X having the probability density function given by: f(x) = 0, for x < -1 k, for -1 â‰¤ x â‰¤ 2 0, for x > 2 a) Find the value of K. b) Find the distribution function of X. c) Find P(0 < X < 1).