# Give a real-life example of data which could have the following probability distributions. Explain your answers. a) normal distribution b) uniform distribution c) exponential distribution a) bimodal distribution Solve this early I upvote b ,c and d only Explain these above three b, c and d

Give a real-life example of data which could have the following probability distributions. Explain your answers. a) normal distribution b) uniform distribution c) exponential distribution a) bimodal distribution Solve this early I upvote b ,c and d only Explain these above three b, c and d
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Step 1. Uniform Distribution Uniform distribution: A continuous random variable X is said to be uniform distribution then the pdf is given by $$f(x)=\begin{cases}\frac{1}{b-a}; & a<x<b = 0\\0 & aterwise\end{cases}$$ Where a and $$b (a<b)$$ are two parametrs of uniform distribution. This is also known as Rectangular distribution. Mean of uniform distribution is $$(b+a)/2$$ and variance is $$(b-a)^{2/12}$$ Example: If you roll a die, you have the chance of getting 1, 2, 3, 4, 5, or 6 and if you rolled it for 3000 times roughly there has a chance of 500 of each result. The results would form a Uniform distribution from 1 to 6. Step 2 Exponential Distribution Exponential distribution: A continuous random variable X is said to be exponential distribution then the pdf is given by $$f(x)= \theta e^{\theta x},x>0, \theta>0$$ Where theta is parameter of exponential distribution. This is also known as Lack of memory distribution. Mean is $$\frac{1}{\theta}$$ and variance is $$1/^2$$ Example: The time it taken to complete graduation of a student with mean 5.2 years then what is the probability it takes more than 4.4 to graduate. The probability density function of exponential distribution is $$f(x)= \theta e^{\theta x},x>0, \theta>0$$
$$p(x\geq4.4)=e^{-4.4/5.2}=0.4290$$ Conclusion : probability it takes more than 4.4 to graduate is 0.4290 Step 3 Bimodal Distributions Bimodal Distribution: In this distribution, ‘Bi’ means two, “Modal” means mode.Bimodal means two modes. Mode is the most frequently repeated value in a set. Example: we take the bimodal age distribution among patients as a graphical representation here the horizontal axis is age of patients and vertical axis is prevalence of disease in the patients.In that 1-st part is 15-34 and second part is 35 & above. Here we have two modes the first repeated set is patients between 15-34 year old and second repeated set is patients between 35 & above.Lets say the patients with 5 year old we found in a population say 5 but we observe 1000 patients and then decrease and again increase here we observe that 15-34 age patients and 35 & above age patients are 1000.This is called bimodal.