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In **Mathematics** / **College** | 2025-08-20

[Answered] 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?

In **Mathematics** / **College** | 2025-08-20

[Answered] Simplify the following: (a) $[7-3 x+10 y-(x-2 y)]-[5 x+2 y-10]$ (b) $\left(y^2-y-1\right)-\left[\frac{1}{2}\left(x-1+2 x^2\right)\right]$ (c) $a b^2+4 a^2 b-3 a^2 b+8 a b^2+5 a b^2+3 a b^2$ (d) $\left(a^2+b^2-2 a b\right)+\left(2 a^2-b^2+a b\right)-\left(a^2-2 b^2+a b\right)$ (e) $\left(3 p^2-2 p-\frac{1}{2}\right)+\left(1-p^2\right)+\left(p^2-6 p\right)+\left(2 p-\frac{5}{2}\right)$ (f) $\left(2 x^2+2 y^2+2 z^2+3 x u z\right)-\left(x^2+y^2+2 x y z+z^2\right)$ (g) $(3 x+5 y-x+2 y)+(5 x+3 y)-(2 y-x+5 x-3 y)$ (h) $(3 x+2 y-9)+(2 x-6 y+2)-[(4 x-9 y-1)+(-3 x+8 y+7)]$

In **History** / **High School** | 2025-08-20

[Answered] How to use these words in a sentence

In **Mathematics** / **High School** | 2025-08-20

[Answered] If [tex]QR=7[/tex], [tex]RS=3x[/tex], and [tex]QS=4x[/tex], what is [tex]QS[/tex]? Simplify your answer and write it as a proper fraction, mixed number, or integer.

In **Mathematics** / **College** | 2025-08-20

[Answered] What is the solution to the linear equation? [tex]4 b+6=2-b+4[/tex]

In **Physics** / **High School** | 2025-08-20

[Answered] An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?

In **History** / **High School** | 2025-08-20

[Answered] Read the excerpt and provide simple and short notes on this section: In September of 2009, Kong Dejun returned to China from her home in Great Britain. The occasion was a birthday celebration for her ancient ancestor Kong Fuzi, or Confucius, born 2,560 years earlier. Together with some 10,000 other people-descendants, scholars, government officials, and foreign representatives-Kong Dejun attended ceremonies at the Confucian Temple in Qufu, the hometown of China's famous sage. "I was touched to see my ancestor being revered by people from different countries and nations,” she said.³ What made this celebration remarkable was that it took place in a country still ruled by the Communist Party, which had long devoted enormous efforts to discrediting Confucius and his teachings. In the communist outlook, Confucianism was associated with class inequality, patriarchy, feudalism, superstition, and all things old and backward. But the country's ancient teacher and philosopher had apparently outlasted modern communism, for now the Communist Party has claimed Confucius as a national treasure and has established over 300 Confucian Institutes to study his writings. He appears in TV shows and movies, and many anxious parents offer prayers at Confucian temples when their children are taking the national college entrance exams. Buddhism and Daoism (DOW-i'zm) have also experienced something of a revival in China, as thousands of temples, destroyed during the heyday of communism, have been repaired and reopened. Christianity too has grown rapidly since the 1970s.

In **Mathematics** / **College** | 2025-08-20

[Answered] [tex]\frac{f}{-4}+11=5[/tex]

In **Mathematics** / **College** | 2025-08-20

[Answered] If $315 is invested at an interest rate of 3% per year and is compounded continuously, how much will the investment be worth in 9 years? Use the continuous compound interest formula: [tex]$A = Pe ^{r t}$[/tex].

In **Mathematics** / **College** | 2025-08-20

[Answered] Which two ordered pairs are solutions for the equation [tex]y=-2 x+4[/tex]? A. (6,-1) B. (1,2) C. (0,4) D. (-2,3)