The discrete random variable X has the probability function given by
[tex]P(X=x)=\left\{\begin{array}{ll} k x & x=2,4,6 \\ k(x-2) & x=8 \\ 0 & \text { Otherwise } \end{array}, \text { Where } k\right.\text { is a constant. }[/tex]
(a) Find [tex]$k$[/tex]
(b) Find [tex]$F(5)$[/tex]
(c) Find [tex]$E[X]$[/tex]
(d) Find [tex]$\operatorname{Var}[3-4 X]$[/tex]
Let X be a discrete random variable with the following probability mass function.
[tex]P_X(x)=\left\{\begin{array}{ll} 0.1 & \text { for } \quad x=0.2 \\ 0.2 & \text { for } \quad x=0.4 \\ 0.2 & \text { for } \quad x=0.5 \\ 0.3 & \text { for } \quad x=0.8 \\ 0.2 & \text { for } \quad x=1.0 \\ 0 & \text { otherwise } \end{array}\right.[/tex]
Find [tex]$P(X=0.2 \mid X\ \textless \ 0.6)$[/tex]
According to the population and housing census conducted by the National Statistical Office, 40% of the Malawians population, 25 years old or above, have completed a bachelor's degree. Given a random sample of 50 Malawians, 25 years old or above.
(a) Mention with reasons the probability distribution to model number of people who have completed bachelor's degree among the 50 people who are 25 years old or above.
(b) What is the expected number of people who have completed a bachelor's degree.
(c) What is the standard deviation of the number of people who have completed a bachelor's degree?
An electronic scale in an automated filling operation stops the manufacturing line after three underweight packages are detected. Suppose that the probability of an underweight package is 0.001 and each fill is independent.
(a) What is the mean number of fills before the line is stopped?
(b) What is the standard deviation of the number of fills before the line is stopped?
The number of failures of a testing instrument from contamination particles on the product is a Poisson random variable with a mean of 0.02 failures per hour. What is the probability that the instrument does not fail in an eight-hour shift?
Hint: [tex]$P(x)=\frac{\theta^x e^{-\theta}}{x!}$[/tex]
The length of stay at specific emergency department has a mean of 4.6 hours with standard deviation of 2.9. Assume that the length of stay is normally distributed.
(a) What is the probability of length of stay greater than 10 hours?
(b) What length of stay is exceeded by 25% of the visits?
Answer (3)
X / 44 = 75 / 100
Do some algebra and X = 33
The number is 33.
75% of 44 is 33.
What is a percentage?
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Number = x
75% of 44
x = 75/100 x 44
x = 3/4 x 44
x = 3 x 11
x = 33
Thus,
75% of 44 is 33.
Learn more about percentages here:
https://brainly.com/question/11403063
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To calculate 75% of 44, first convert 75% to a decimal (0.75) and then multiply it by 44, resulting in 33. Therefore, 75% of 44 is 33.
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