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# System prepended metadata

title: Statistics
tags: [questions]

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layout: default
date: 2018-05-25
tags: questions
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# Statistics

1. How do you set limits?
2. What is binned and unbinned likelihood fit? Which is better to use?
3. How the limits of two different analysis are combined?
4. Why use fit function?
1. **If signal strength, ($\mu<1$), do you think you overestimated some/any of your background?**

1. Calorimetry resolution $$\frac{\sigma_E}{E} = \frac{a}{\sqrt{E}} + \frac{b}{E} + C$$, Explain various coeficients.

    a $\rightarrow$ **Stochastic term:** It includes contribution from shower containments, number of photoelectrons, fluctuations in the gain process.
    
    b $\rightarrow$ **Noise term**
    
    c $\rightarrow$ **Constant term:** Dominates for high energy electrons and photon showers, depends on non-uniformity of longitudinal light collenction, energy leakage from back of calorimeter, single channel response uniformity and stability.
    
    **In homogeneous calorimeters**, main sources of energy uncertanity are
        
        1. shower fluctuations,
        2. phooto electron statistics
        3. shower leakage
        4. Instrumental effects (like noise, light attenuations, non-uniformity)

    In addition of these, in **sampling calorimeters**, there are some other effects as well. They are:
        
        1. sampling fluctuations,
        2. landau fluctuations,
        3. track length fluctuations.

    Variation of different fluctuations:
    
        1. Quantum fluctuations ~ $1/\sqrt{E}$
        2. Electronics noise ~ $1/E$
        3. shower leakage ~ const.
        4. sampling fluctuations ~ $1/\sqrt{E}$
        5. Landau fluctuations ~ $1/\sqrt{E}$
        6. Track length fluctuations ~ $1/\sqrt{E}$