1. The functions sinh, cosh, tanh are defined by Joos sn 0/2 e e cosh(ar) 2 e2 -ez sinh(a) 2 loosh sinh sinh(r) Cosh(r) e tanh(r) e e- are often referred to as hyperbolic trig functions (the figure above gives some sense why). Pronunciation tips: cosh rhymes with gosh, sinh with pinch, and tanh with ranch. The other hyperbolic trig functions are sech (r) = conh(# » C$ch (#) = inh(@} » Coth(x) = ianh ° (a) Find some identities for hyperbolic trig functions, showing justification (hint: compare to common identities for trig functions) e coth(z)da (b) Evaluate sinh(r) cosh(a) dæ (c) Evaluate (d) Evaluate cosh(r)dr (e) (Optional) Inverses of the hyperbolic trig functions are defined on appropriate domains, and may be expressed in terms of logarithms, for example arcosh(r) n (r+ Vx2 =1) ;x >1 In( x+ Vx2+1);-oo< < 00 arsinh(r) 1 In artanh(r) Use substitutions with hyperbolic trig functions (and a corresponding identity from part (a)) to evaluate -dr and V2+1

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Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.