Probability Distribution | Probability Mass Function | Probability Histogram | C . D . F & Spider

A tubular Arrangement in against each value of Discrete Random Variable its Probability occurred is called Discrete Probability Distribution and its function is called probability Mass function A function which cumulates probabilities from lower limit up to specific value of X is called Cumulative Distribution function and it’s graph is called Spider Graph #probabilitydistribution #probabilitymassfunction Probability Mass Function (PMF) Definition: The PMF gives the probability that a discrete random variable takes on the value . Properties: 1. for all X P(X) +ve 2. The sum of probabilities for all possible values equals 1: 3. €P(X = x) = 1. Cumulative Distribution Function (CDF) Definition: The CDF of a random variable gives the probability that is less than or equal to specific value of X. Graphs of PMF and CDF PMF Graph: Appearance: A bar graph where each bar represents the probability for a specific value of . Key Feature: Shows the discrete probability distribution explicitly. CDF Graph: Appearance: A step-like graph that increases at each value of by . Probability Distribution A probability distribution describes how the probabilities of a random variable are distributed across its possible values. It can be expressed as: 1. Discrete Probability Distribution (PMF): Lists all possible values of a discrete random variable along with their corresponding probabilities. 2. Continuous Probability Distribution (PDF): For continuous random variables, the distribution is represented using a Probability Density Function (PDF). The area under the curve of the PDF between two points gives the probability of the variable falling in that interval. Total area under the curve = 1. Would you like a worked example or an explanation of any specific type of distribution (e.g., normal, binomial)? In This chapter we Discuss in Detail... https://youtu.be/Z3s24CxOP78?si=LxXQZN8SSg6DGQo7 https://youtu.be/vpwFWXPQpJI?si=DN6ZRcWTXg5OzcuY https://youtu.be/W51FxJ-Ccik?si=fDbG-q96ZN3LpPTB https://youtu.be/asDMDEYUgUE?si=qlNaB2mRvIgAKILB https://youtu.be/PwvNXC7Yvv0?si=oSdUL_rnI1KlLCO7 https://youtu.be/sXjgAamey7M?si=5fMOfJfGKz4Fk8X0 https://youtu.be/xPeMtigdCCw?si=aamHYf8iWRgmiEJW https://youtu.be/DLIJ7YIZK1A?si=JYEjR1vT4xRGQqCv https://youtu.be/oKmpimdXYGg?si=N5fx4i0gI_mUwvyW https://youtu.be/jc_2WbIQ3iY?si=r1w-dh4JYBtZSsW9 https://youtu.be/xY0uYbRk7vc?si=I2gUE84SR8FqiJPs https://youtu.be/-cUw4cTJFFk?si=XylGQCJQGJI5YUVG Random Variables #randomexperiment #randomvariable #probabilitydistribution #pmf #pdf #cdf #probabilitymassfunction #probabilitydensityfunction #cumulativedostributionfunction #expectation #mathematicalexpectation #propertiesofexpectation #bivariateprobabilitydistribution #bivariatepmf #statisticalindependence #momentgeneratingfunction #propertiesofmgf #characteristicgeneratingfunction #correlationinrandomvariables #jointpdf #jointpmf #randomnumbers #howrandomnumbersgenerated #usesofranfomnumbers #transformation Links Play List https://youtube.com/@Mstatistics?si=g4WZatoeiGtGxE2Y https://youtube.com/playlist?list=PLE6FeA-mAm2cw0QJvkmDtXSuFMOcyR22k&si=cFZMBQXx3-NsxEFs https://youtube.com/playlist?list=PLE6FeA-mAm2ckQ2g3PbZa3JFcS7Dch6zH&si=d8tX6T5bikR9ZOvT https://youtube.com/playlist?list=PLE6FeA-mAm2fC2vBS9Tsm1pNq0jrHRBRN&si=Z1xXtYnu3ZLghz2L https://youtube.com/playlist?list=PLE6FeA-mAm2cTiJSRpFQXUXxnwPRnMYd2&si=fwbLBOwb9OZ7KvcT https://youtube.com/playlist?list=PLE6FeA-mAm2cJBSS7MFtY_qNt0S98LrUf&si=xeKv_QM2eETnFtHs https://youtube.com/playlist?list=PLE6FeA-mAm2fN6DP_jOvUmd-Vz7JRCCju&si=APcCUnxh3-09A1vK https://youtube.com/playlist?list=PLE6FeA-mAm2enYtyM0hNZwwkeiDk9_U-n&si=WsmS9fHwFAHWUc9m https://youtube.com/playlist?list=PLE6FeA-mAm2c09AkhYm67o80t3QmDFlUe&si=cUux7KQiJtMm_zqf https://youtube.com/playlist?list=PLE6FeA-mAm2f8b5z-TB-Xa2LaVW-4RlOB&si=xg0ykFRadIZ9ROSi https://youtube.com/playlist?list=PLE6FeA-mAm2e2W1skwNMXb-pAIabRg87w&si=qZ2syfTp0o7mVQjF https://youtube.com/playlist?list=PLE6FeA-mAm2ep0-7j0_5rUjOiO5khbIMe&si=YJ9fRiDw9c_0kQv1 https://youtube.com/playlist?list=PLE6FeA-mAm2eOw--_Qx6fI74O30PdHgOR&si=WLTgwi1S5RY7EuCO https://youtube.com/playlist?list=PLE6FeA-mAm2fPYYT9uC7OJW_qLiDaQRru&si=8bzkAdH1r9FNlJVT https://youtube.com/playlist?list=PLE6FeA-mAm2ePUb5xru9NFGVvT8rYV-KB&si=5ePtgzTDDaxwb1RZ https://youtube.com/playlist?list=PLE6FeA-mAm2elLeIiEJRKDXhQhYQ2GKgg&si=5QXO6vckhfVLejYL https://youtube.com/playlist?list=PLE6FeA-mAm2fyU7Rjk_B4nHMw-jzzf_1A&si=qNftTMbZ137sz5L3 https://youtube.com/playlist?list=PLE6FeA-mAm2c6lj4Fh08DgfZd6YirTqcA&si=-4wtZjdZrbE6vGqK https://youtube.com/playlist?list=PLE6FeA-mAm2csE5-qXt-MHRlmDzsC3E1m&si=YgOCBQq_gQyEQ4Cj https://youtube.com/playlist?list=PLE6FeA-mAm2fszoMIzaEtjqDZgWrxG2Ff&si=DJSuWXIJldNeBxLy https://youtube.com/playlist?list=PLE6FeA-mAm2d7nig0ltxb7c9RhtVnVLVE&si=6JvgcHLtHPysO_Cc https://youtube.com/playlist?list=PLE6FeA-mAm2fwvWmbbgjwuJ2krHcUV4uF&si=7WcT2fYG8Bo11NnB